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Dissertations / Theses on the topic 'Moduli space'
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1
Hakimi, Koopa. "Moduli space of sheaves on fans." Thesis, University of British Columbia, 2011. http://hdl.handle.net/2429/33974.
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A conjecture of H. Hopf states that if x(M²n) is a closed, Riemannian manifold of nonpositive sectional curvature, then its Euler characteristic x(M²n), should satify (-1)n x(M²n)≥ 0. Ruth Charney and Michael Davis investigated the conjecture in the context of piecewise Euclidean manifolds having "nonpositive curvature" in the sense of Gromov's CAT(0) inequality. In that context the conjecture can be reduced to a local version which predicts the sign of a "local Euler characteristic" at each vertex. They stated precisely various conjectures in their paper which we are interested in one of them stated as Conjecture D (see [1]) which is equivalent to the Hopf Conjecture for piecewise Euclidean manifolds cellulated by cubes.
The goal of this thesis is to study the Charney - Davis Conjecture stated as Conjecture (D) by using sheaves on fans.
2
Dotti, Gustavo. "The moduli space of supersymmetric guage theories /." Diss., Connect to a 24 p. preview or request complete full text in PDF format. Access restricted to UC IP addresses, 1998. http://wwwlib.umi.com/cr/ucsd/fullcit?p9824648.
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Hønsen, Morten Oskar 1973. "A compact moduli space for Cohen-Macaulay curves in projective space." Thesis, Massachusetts Institute of Technology, 2004. http://hdl.handle.net/1721.1/28826.
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Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Mathematics, 2004.Includes bibliographical references (p. 57-59).
We define a moduli functor parametrizing finite maps from a projective (locally) Cohen-Macaulay curve to a fixed projective space. The definition of the functor includes a number of technical conditions, but the most important is that the map is almost everywhere an isomorphism onto its image. The motivation for this definition comes from trying to interpolate between the Hilbert scheme and the Kontsevich mapping space. The main result of this thesis is that our functor is represented by a proper algebraic space. As an application we obtain interesting compactifications of the spaces of smooth curves in projective space. We illustrate this in the case of rational quartics, where the resulting space appears easier than the Hilbert scheme.
by Morten Oskar Hønsen.
Ph.D.
4
Mandini, Alessia <1979>. "The geometry of the moduli space of polygons in the euclidean space." Doctoral thesis, Alma Mater Studiorum - Università di Bologna, 2007. http://amsdottorato.unibo.it/424/1/Tesi_A._Mandini.pdf.
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Mandini, Alessia <1979>. "The geometry of the moduli space of polygons in the euclidean space." Doctoral thesis, Alma Mater Studiorum - Università di Bologna, 2007. http://amsdottorato.unibo.it/424/.
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Fortin, Boisvert Mélisande. "Cycles on the moduli space of hyperelliptic curves." Thesis, McGill University, 2003. http://digitool.Library.McGill.CA:80/R/?func=dbin-jump-full&object_id=78361.
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Oort gave a complete description of symplectic commutative group schemes killed by p and of rank p2g . Each such group appears as the p-torsion group scheme of some principally polarized abelian variety and this classification can be given in terms of final sequences. In this thesis, we focus on the particular situation where the abelian variety is the Jacobian of a hyperelliptic curve. We concentrate on describing the subspace of the moduli space of hyperelliptic curves, or rather the cycle, corresponding to a given final sequence. Especially, we concentrate on describing the subspace corresponding to the non-ordinary locus, which is a union of final sequences.
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Hausel, TamaÌs. "Geometry of the moduli space of Higgs bundles." Thesis, University of Cambridge, 1998. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.397444.
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Dwivedi, Shashank S. (Shashank Shekhar). "Towards birational aspects of moduli space of curves." Thesis, Massachusetts Institute of Technology, 2010. http://hdl.handle.net/1721.1/62454.
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Thesis (S.M.)--Massachusetts Institute of Technology, Dept. of Electrical Engineering and Computer Science, 2010.Cataloged from PDF version of thesis.
Includes bibliographical references (p. 43-46).
The moduli space of curves has proven itself a central object in algebraic geometry. The past decade has seen substantial progress in understanding its geometry. This has been spurred by a flurry of ideas from geometry (algebraic, symplectic, and differential), topology, combinatorics, and physics. One way of understanding its birational geometry is by describing its cones of ample and effective divisors and the dual notion of the Mori cone (the closed cone of curves). This thesis aims at giving a brief introduction to the moduli space of n-pointed stable curves of genus ... and some intuition into it and its structure. We do so by surveying what is currently known about the ample and the effective cones of ... , and the problem of determining the closed cone of curves ... The emphasis in this exposition lies on a partial resolution of the Fulton-Faber conjecture (the F-conjecture). Recently, some positive results were announced and the conjecture was shown to be true in a select few cases. Conjecturally, the ample cone has a very simple description as the dual cone spanned by the F-curves. Faber curves (or F-curves) are irreducible components of the locus in ... that parameterize curves with 3g - 4 + n nodes. There are only finitely many classes of F-curves. The conjecture has been verified for the moduli space of curves of small genus. The conjecture predicts that for large g, despite being of general type, ... behaves from the point of view of Mori theory just like a Fano variety. Specifically, this means that the Mori cone of curves is polyhedral, and generated by rational curves. It would be pleasantly surprising if the conjecture holds true for all cases. In the case of the effective cone of divisors the situation is more complicated. F-conjecture. A divisor on ... is ample (nef) if and only if it intersects positively (nonnegatively) all 1-dimensional strata or the F-curves . In other words, every extremal ray of the Mori cone of effective curves NE1(Mg,n) is generated by a one dimensional stratum. The main results presented here are: (i) the Mori cone ... is generated by F-curves when ...
by Shashank S. Dwivedi.
S.M.
9
Zaw, Myint. "The moduli space of non-classical directed Klein surfaces." Bonn : [s.n.], 1998. http://catalog.hathitrust.org/api/volumes/oclc/41464662.html.
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Farkas, Gavril Marius. "The birational geometry of the moduli space of curves." [S.l. : Amsterdam : s.n.] ; Universiteit van Amsterdam [Host], 2000. http://dare.uva.nl/document/84192.
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Tsukamoto, Masaki. "The geometry of the moduli space of Brody curves." 京都大学 (Kyoto University), 2008. http://hdl.handle.net/2433/136951.
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Xia, Bingyu. "Moduli spaces of Bridgeland semistable complexes." The Ohio State University, 2017. http://rave.ohiolink.edu/etdc/view?acc_num=osu1491824968521162.
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Pavel, Mihai-Cosmin. "Moduli spaces of semistable sheaves." Electronic Thesis or Diss., Université de Lorraine, 2022. http://www.theses.fr/2022LORR0125.
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Dans cette thèse nous construisons des espaces de modules de faisceaux semi-stables sur une variété projective complexe lisse X, dotée d'une polarisation fixée sheaf{O}_X(1). Notre approche suit les idées de Le Potier et Jun Li, qui ont construit indépendamment des espaces de modules de faisceaux sans torsion, semi-stables par rapport à la pente sur des surfaces (projectives). Leurs espaces sont en relation, par la correspondance Kobayashi-Hitchin, avec la compactification de Donaldson-Uhlenbeck en théorie de jauge. Ici, cependant, nous sommes principalement intéressés par les aspects algébriques de leur travail. En particulier, cette thèse généralise leur construction au cas des faisceaux purs de dimension supérieure, dont le schéma de support peut être singulier. Nous introduisons d'abord une notion de stabilité pour les faisceaux cohérents purs de dimension d sur X, qui se situe entre la stabilité par rapport à la pente et la stabilité de Gieseker. Cette notion est définie par rapport au polynôme de Hilbert du faisceau, tronqué jusqu'à un certain degré. Nous l'appelons ell-(semi)stabilité, où ell marque le niveau de troncature. En particulier, on retrouve la notion classique de stabilité par rapport à la pente pour ell = 1 et de Gieseker-stabilité pour ell = d. Notre construction utilise comme ingrédient principal un théorème de restriction pour la (semi-)stabilité, disant que la restriction d'un faisceau ell-semistable (ou ell-stable) à un diviseur général D in |sheaf{O}_X(a)| de degré suffisamment grand dans X est à nouveau ell-semistable (respectivement ell-stable). À cet égard, dans le Chapitre 2, nous prouvons plusieurs théorèmes de restriction pour les faisceaux purs (voir les Théorèmes ef{thm:GiesekerRestriction},ef{thm:restrictionStable} etef{thm:ThmC}). Les méthodes utilisées dans la preuve nous permettent de donner des énoncés en caractéristique quelconque. De plus, nos résultats généralisent les théorèmes de restriction de Mehta et Ramanathan pour la (semi-)stabilité par rapport à la pente, et ils s'appliquent en particulier aux faisceaux Gieseker-semistables. Avant de donner la construction, nous faisons un bref détour pour généraliser la fibration d'Iitaka classique au cadre équivariant. Nous construisons alors des espaces de modules projectifs de faisceaux ell-semistables en dimensions supérieures, comme certaines fibrations d'Iitaka équivariantes (voir le Théorème~ef{thm:mainThm}). Notre construction est nouvelle dans la littérature lorsque 1 < ell < d ou lorsque ell=1 et d < dim(X). En particulier, dans le cas des faisceaux sans torsion, nous récupérons un résultat de Huybrechts-Lehn sur les surfaces et de Greb-Toma en dimensions supérieures. Enfin, nous décrivons en détail les points géométriques de ces espaces de modules (voir le Théorème~ef{thm:separation}). Comme application, nous montrons que dans le cas sans torsion, ils fournissent des compactifications différentes sur le lieu ouvert des fibrés vectoriels stables par rapport à la pente. Nous pouvons considérer ces espaces comme des compactifications intermédiaires entre la compactification de Gieseker et la compactification de Donaldson-UhlenbeckIn this thesis we construct moduli spaces of semistable sheaves over a complex smooth projective variety X, endowed with a fixed polarization sheaf{O}_X(1). Our approach is based on ideas of Le Potier and Jun Li, who independently constructed moduli spaces of slope-semistable torsion-free sheaves over (projective) surfaces. Their spaces are closely related, via the Kobayashi-Hitchin correspondence, to the so-called Donaldson-Uhlenbeck compactification in gauge theory. Here, however, we are mainly interested in the algebraical aspects of their work. In a restrictive sense, this thesis generalizes their construction to higher dimensional pure sheaves, whose support scheme might be singular. First we introduce a notion of stability for pure coherent sheaves of dimension d on X, which lies between slope- and Gieseker-stability. This is defined with respect to the Hilbert polynomial of the sheaf, truncated down to a certain degree. We call it ell-(semi)stability, where ell marks the level of truncation. In particular, this recovers the classical notion of slope-stability for ell =1 and of Gieseker-stability for ell = d. Our construction uses as main ingredient a restriction theorem for (semi)stability, saying that the restriction of an ell-semistable (or ell-stable) sheaf to a general divisor D in |sheaf{O}_X(a)| of sufficiently large degree in X is again ell-semistable (respectively ell-stable). In this regard, in Chapter~ef{ch:RestrictionTheorems} we prove several restriction theorems for pure sheaves (see Theorems~ef{thm:GiesekerRestriction},ef{thm:restrictionStable} and ef{thm:ThmC}). The methods employed in the proofs permit us to give statements in arbitrary characteristic. Furthermore, our results generalize the restriction theorems of Mehta and Ramanathan for slope-(semi)stability, and they apply in particular to Gieseker-semistable sheaves. Before we give the construction, we take a short detour to generalize the classical Iitaka fibration to the equivariant setting. Given this, we construct projective moduli spaces of ell-semistable sheaves in higher dimensions as certain equivariant Iitaka fibrations (see Theorem~ef{thm:mainThm}). Our construction is new in the literature when 1
14
Forcella, Davide. "Moduli Space and Chiral Ring of D3 Branes at Singularities." Doctoral thesis, SISSA, 2008. http://hdl.handle.net/20.500.11767/4837.
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StClair, Jessica Lindsey. "Geometry of Spaces of Planar Quadrilaterals." Diss., Virginia Tech, 2011. http://hdl.handle.net/10919/26887.
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The purpose of this dissertation is to investigate the geometry of spaces of planar quadrilaterals.
The topology of moduli spaces of planar quadrilaterals (the set of all distinct planar
quadrilaterals with fixed side lengths) has been well-studied [5], [8], [10]. The symplectic
geometry of these spaces has been studied by Kapovich and Millson [6], but the Riemannian
geometry of these spaces has not been thoroughly examined. We study paths in the moduli
space and the pre-moduli space. We compare intraplanar paths between points in the moduli
space to extraplanar paths between those same points. We give conditions on side lengths
to guarantee that intraplanar motion is shorter between some points. Direct applications of
this result could be applied to motion-planning of a robot arm. We show that horizontal lifts
to the pre-moduli space of paths in the moduli space can exhibit holonomy. We determine
exactly which collections of side lengths allow holonomy.Ph. D.
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Meachan, Ciaran. "Moduli of Bridgeland-Stable objects." Thesis, University of Edinburgh, 2012. http://hdl.handle.net/1842/6230.
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In this thesis we investigate wall-crossing phenomena in the stability manifold of an irreducible principally polarized abelian surface for objects with the same invariants as (twists of) ideal sheaves of points. In particular, we construct a sequence of fine moduli spaces which are related by Mukai flops and observe that the stability of these objects is completely determined by the configuration of points. Finally, we use Fourier-Mukai theory to show that these moduli are projective.
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Singh, D. "The moduli space of stable N pointed curves of genus zero." Thesis, University of Sheffield, 2004. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.414682.
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Slavov, Kaloyan (Kaloyan Stefanov). "The moduli space of hypersurfaces whose singular locus has high dimension." Thesis, Massachusetts Institute of Technology, 2011. http://hdl.handle.net/1721.1/64605.
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Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Mathematics, 2011.Cataloged from PDF version of thesis.
Includes bibliographical references (p. 75).
Fix integers n and b with n =/> 3 and 1 =/< b < n - 1. Let k be an algebraically closed field. Consider the moduli space X of hypersurfaces in P" of fixed degree I whose singular locus is at least b-dimensional. We prove that for large 1, X has a unique irreducible component of maximal dimension, consisting of the hypersurfaces singular along a linear b-dimensional subspace of P".
by Kaloyan Slavov.
Ph.D.
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Sugiyama, Toshi. "The Moduli Space of Polynomial Maps and Their Fixed-Point Multipliers." Kyoto University, 2018. http://hdl.handle.net/2433/233819.
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Wimelaratna, Ramasinghege. "Multi dimensional geometric moduli and exterior algebra of a Banach space /." The Ohio State University, 1988. http://rave.ohiolink.edu/etdc/view?acc_num=osu148759830383865.
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Murri, Riccardo. "Computational techniques in graph homology of the moduli space of curves." Doctoral thesis, Scuola Normale Superiore, 2013. http://hdl.handle.net/11384/85723.
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The object of this thesis is the automated computation of the rational (co)homology
of the moduli spaces of smooth marked Riemann surfaces Mg;n. This is achieved by
using a computer to generate a chain complex, known in advance to have the same
homology as Mg;n, and explicitly spell out the boundary operators in matrix form.
As an application, we compute the Betti numbers of some moduli spaces Mg;n.
Our original contribution is twofold. In Chapter 3, we develop algorithms for the
enumeration of fatgraphs and their automorphisms, and the computation of the
homology of the chain complex formed by fatgraphs of a given genus g and number
of boundary components n.
In Chapter 4, we describe a new practical parallel algorithm for performing Gaussian
elimination on arbitrary matrices with exact computations: projections indicate
that the size of the matrices involved in the Betti number computation can easily
exceed the computational power of a single computer, so it is necessary to distribute
the work over several processing units. Experimental results prove that our
algorithm is in practice faster than freely available exact linear algebra codes.
An effective implementation of the fatgraph algorithms presented here is available
at http://code.google.com/p/fatghol. It has so far been used to compute the Betti
numbers of Mg;n for (2g + n) 6 6.
The Gaussian elimination code is likewise publicly available as open-source software
from http://code.google.com/p/rheinfall.
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KONDO, SHIGEYUKI. "On the Kodaira Dimension of the Moduli Space of K3 Surfaces II." Cambridge University Press, 1999. http://hdl.handle.net/2237/10252.
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Camara, Malick. "Tautological rings of moduli spaces of curves." Thesis, Paris 6, 2016. http://www.theses.fr/2016PA066459.
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Les espaces de modules de Riemann répondent au problème de la classification des surfaces de Riemann compactes d'un genre donné. Le sujet de cette thèse est la cohomologie de l'espace des modules des courbes d'un genre donné avec un certain nombre de points marqués. La description de cet anneau a été initiée par D. Mumford puis C. Faber avait proposé une description de l'anneau tautologique des espaces de modules sans points marqués. Une première source de relations provient des relations A. Pixton démontrées par A. Pixton, R. Pandharipande et D. Zvonkine mais on ne sait pas si elles sont complètes. Une autre source de relations utilisée dans ce travail sont les relations de A. Buryak, S. Shadrin et D. Zvonkine. Avant cette thèse, il y avait peu de résultats sur l'anneau tautologique d'espaces de modules de courbes avec un nombre quelconque de points marqués. Cette thèse donne une description complète des l'anneaux tautologiques des espaces de modules de courbes de genres 0, 1, 2, 3 et 4. Un des résultats ayant demandé beaucoup de travail est le groupe de degré 2 de l'anneau tautologique des espaces de modules de courbes lisses de genre 4. Ce groupe demande un travail sur l'annulation de certaines classes tautologiques sur le bord de la compactification de Deligne-Mumford de l'espace des modules en plus d'un astucieux travail numérique. L'espace des modules des courbes réelles de genre 0 et sa théorie de l'intersection sont également étudiés. On peut alors démontrer plusieurs résultats analogues à ceux obtenus dans le cas complexe comme l'équation de la corde. On démontre une formule donnant les nombres d'intersectionThe problem of the moduli spaces of compact Riemann surfaces is the problem of the classification of compact Riemann surfaces of a certain genus. The topic of this thesis is the cohomology of the moduli spaces of curves of a certain genus with marked points and more precisely its subbring called tautological ring. The description of the tautological ring has been initiated by D. Mumford, then C. Faber conjectured a description of the moduli space of curves without marked points. A source of tautological relations are Pixton's relations proven by A. Pixton, R. Pabndharipande and D. Zvonkine. Another source of relations are relations of A. Buryak, S. Shadrin and D. Zvonkine. Before this thesis, there were only few results on the tautological ring of curves with any number of marked points. This thesis gives a complete description of the tautological rings of moduli curves of genera 0, 1, 2, 3 and 4 with any number of marked points. A result which needed a lot of work is the group of degree 2 of the tautological ring of the moudli space of smooth curves of genus 4. We need to work on the vanishing of some tautological classes on the boundary of the Deligne-Mumford compactification of the moduli space of curves and a clever numerical work.The moduli space of real curves of genus 0 and its intersection theory are also studied. Then we can show several results which are analogous to results in the complex case like the string equation. One result of this thesis is a formula giving intersection numbers of products of xi classes.x
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Ying, Daniel. "On the Moduli Space of Cyclic Trigonal Riemann Surfaces of Genus 4." Doctoral thesis, Linköping : Matematiska institutionen, Linköpings universitet, 2006. http://urn.kb.se/resolve?urn=urn:nbn:se:liu:diva-8237.
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Kalveks, Rudolph. "Group symmetries and the moduli space structures of SUSY quiver gauge theories." Thesis, Imperial College London, 2016. http://hdl.handle.net/10044/1/52710.
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This thesis takes steps towards the development of a systematic account of the relationships between SUSY quiver gauge theories and the structures of their moduli spaces. Highest Weight Generating functions (“HWGs”), which concisely encode the field content of a moduli space, are introduced and developed to augment the established plethystic techniques for the construction and analysis of Hilbert series (“HS”). HWGs are shown to provide a faithful means of decoding and describing HS in terms of their component fields, which transform in representations of Classical and/or Exceptional symmetry groups. These techniques are illustrated in the context of Higgs branch quiver theories for SQCD and instanton moduli spaces, as a prelude to an account of the quiver theory constructions for the canonical class of moduli spaces represented by the nilpotent orbits of Classical and Exceptional symmetry groups. The known Higgs and/or Coulomb branch quiver theory constructions for nilpotent orbits are systematically extended to give a complete set of Higgs branch quiver theories for Classical group nilpotent orbits and a set of Coulomb branch constructions for near to minimal orbits of Classical and Exceptional groups. A localisation formula (“NOL Formula”) for the normal nilpotent orbits of Classical and Exceptional groups based on their Characteristics is proposed and deployed. Dualities and other relationships between quiver theories, including A series 3d mirror symmetry, are analysed and discussed. The use of nilpotent orbits, for example in the form of T(G) quiver theories, as building blocks for the systematic (de)construction of moduli spaces is illustrated. The roles of orthogonal bases, such as characters and Hall Littlewood polynomials, in providing canonical structures for the the analysis of quiver theories is demonstrated, along with their potential use as building blocks for more general families of quiver theories.
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Ruoff, Fabian [Verfasser], and F. [Akademischer Betreuer] Herrlich. "The Moduli Space of Algebraic Translation Surfaces / Fabian Ruoff ; Betreuer: F. Herrlich." Karlsruhe : KIT-Bibliothek, 2021. http://nbn-resolving.de/urn:nbn:de:101:1-2021091505002271869645.
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Maienschein, Thomas Daniel. "Desingularizing the boundary of the moduli space of genus one stable quotients." Diss., The University of Arizona, 2014. http://hdl.handle.net/10150/325213.
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The moduli space of stable quotients, introduced by Marian, Oprea, and Pandharipande, provides a nonsingular compactification of the moduli space of degree d maps from smooth genus 1 curves into projective space ℙⁿ. This is done by allowing the domain curve to have nodal singularities and by admitting certain rational maps. The rational maps are introduced in the following way: A map to projective space can be defined by a quotient bundle of the trivial bundle on the domain curve; in the compactification, the quotient bundle is replaced by a sheaf which may not be locally free. The boundary is filtered by the degree of the torsion subsheaf of the quotient. Yijun Shao has defined a similar compactification of the moduli space of degree d maps from ℙ¹ into a Grassmannian. A blow-up process is carried out on the compactification in order to produce a boundary which is a simple normal crossings divisor: The closed subschemes in the filtration of the boundary are blown up in order of decreasing torsion. In this thesis, we carry out an analogous blow-up process on the moduli space of stable quotients. We show that the end result is a nonsingular compactification which has as its boundary a simple normal crossings divisor.
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Larsen, Paul L. "Applied Mori theory of the moduli space of stable pointed rational curves." Doctoral thesis, Humboldt-Universität zu Berlin, Mathematisch-Naturwissenschaftliche Fakultät II, 2011. http://dx.doi.org/10.18452/16330.
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Diese Dissertation befasst sich mit Fragen über den Modulraum M_{0,n} der stabilen punktierten rationalen Kurven, die durch das Mori-Programm motiviert sind. Insbesondere studieren wir den nef-Kegel (Chapter 2), den Cox-Ring (Chapter 3), und den Kegel der beweglichen Kurven (Chapter 4). In Kapitel 2 beweisen wir Fultons Vermutung für M_{0,n}, nWe investigate questions motivated by Mori''s program for the moduli space of stable pointed rational curves, M_{0,n}. In particular, we study its nef cone (Chapter 2), its Cox ring (Chapter 3), and its cone of movable curves (Chapter 4). In Chapter 2, we prove Fulton''s conjecture for M_{0,n} for n less than or equal to 7, which states that any divisor on these moduli spaces non-negatively intersecting all so-called F-curves is linearly equivalent to an effective sum of boundary divisors. As a corollary, it follows that a divisor is nef if and only if the divisor intersects all F-curves non-negatively. By duality, we thus recover Keel and McKernan''s result that the F-curves generate the closed cone of curves when n is less than or equal to seven, but with methods that do not rely on negativity properties of the canonical bundle that fail for higher n. Chapter 3 initiates a study of relations among generators of the Cox ring of M_{0,n}. We first prove a `relation-free'' result that exhibits polynomial subrings of the Cox ring in boundary section variables. In the opposite direction, we exhibit multidegrees such that the corresponding graded parts meet the ideal of relations non-trivially. In Chapter 4, we study the so-called complete intersection cone for the three-fold M_{0,6}. For a smooth projective variety X, this cone is defined as the closure of curve classes obtained as intersections of the dimension of X minus one very ample divisors. The complete intersection cone is contained in the cone of movable curves, which is dual to the cone of pseudoeffective divisors. We show that, for a series of toric birational models for M_{0,6}, the complete intersection and movable cones coincide, while for M_{0,6}, there is strict containment.
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Fedosov, Boris. "Moduli spaces and deformation quantization in infinite dimensions." Universität Potsdam, 1998. http://opus.kobv.de/ubp/volltexte/2008/2539/.
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We construct a deformation quantization on an infinite-dimensional symplectic space of regular connections on an SU(2)-bundle over a Riemannian surface of genus g ≥ 2. The construction is based on the normal form thoerem representing the space of connections as a fibration over a finite-dimensional moduli space of flat connections whose fibre is a cotangent bundle of the infinite-dimensional gauge group. We study the reduction with respect to the gauge groupe both for classical and quantum cases and show that our quantization commutes with reduction.
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Intwala, Jay D. "Solid State Data Recorder (SSDR) for Airborne/Space Environment." International Foundation for Telemetering, 1993. http://hdl.handle.net/10150/611894.
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International Telemetering Conference Proceedings / October 25-28, 1993 / Riviera Hotel and Convention Center, Las Vegas, NevadaVME bus has been widely accepted as an industry standard for control and process computers. The MSTI (Miniature Sensor Technology Integration) series of satellites employ a VME bus based data acquisition and control system. This system requires a ruggedized, high-speed, compact, low power and light weight data recorder for storing digital imagery from payload video cameras, as well as health and status data of the satellite. No commercial off the shelf systems were found which meet MSTI specifications. Also, a solid state device eliminates certain reliability and spacecraft pointing control problems which are encountered when using rotating (disk or tape) storage systems. The SSDR was designed to meet these requirements and it also has built-in flexibility for many general purpose applications. The electronic hardware design, which conforms to the VME bus specifications [1], can also be configured as stand-alone system. Modular memory array design allows expandability of capacity up to 320 MBytes. This paper will describe the design features of the SSDR. Performance capabilities and system implementation will be discussed. Special approaches required for application of the SSDR in space or harsh environments are also discussed.
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Biroth, Laura [Verfasser]. "Integrable systems and a moduli space for (1,6)-polarised abelian surfaces / Laura Biroth." Mainz : Universitätsbibliothek Mainz, 2019. http://d-nb.info/1200661478/34.
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Solomon, Jake P. (Jake Philip). "Intersection theory on the moduli space of holomorphic curves with Lagrangian boundary conditions." Thesis, Massachusetts Institute of Technology, 2006. http://hdl.handle.net/1721.1/34551.
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Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Mathematics, 2006.Includes bibliographical references (p. 107-109).
We define a new family of open Gromov-Witten type invariants based on intersection theory on the moduli space of pseudoholomorphic curves of arbitrary genus with boundary in a Lagrangian submanifold. We assume the Lagrangian submanifold arises as the fixed points of an anti-symplectic involution and has dimension 2 or 3. In the strongly semi-positive genus 0 case, the new invariants coincide with Welschinger's invariant counts of real pseudoholomorphic curves. Furthermore, we calculate the new invariant for the real quintic threefold in genus 0 and degree 1 to be 30. The techniques we introduce lay the groundwork for verifying predictions of mirror symmetry for the real quintic.
by Jake P. Solomon.
Ph.D.
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CORNIANI, ELSA. "Compattificazioni wonderful e spazi di moduli di Kontsevich di coniche." Doctoral thesis, Università degli studi di Modena e Reggio Emilia, 2022. http://hdl.handle.net/11380/1265207.
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In questa tesi studiamo alcune varietà algebriche dal punto di vista della geometria birazionale. Data una varietà vogliamo descrivere tutti i suoi modelli birazionali. In generale questo è un problema molto difficile, ma per una classe speciale di varietà, chiamate Mori dream spaces, la geometria birazionale è codificata in una decomposizione in insiemi convessi del loro cono effettivo. I Mori dream spaces sono stati introdotti da Y. Hu e S. Keel e sono chiamati così poiché si comportano nel miglior modo possibile dal punto di vista del programma dei modelli minimali.
La prima parte della tesi è dedicata alla costruzione di compattificazioni wonderful di spazi di mappe lineari. Riprendiamo la costruzione, dovuta a I. Vainsencher, degli spazi delle collineazioni e delle quadriche complete di rango massimo e poi la generalizziamo a spazi di mappe lineari di qualsiasi rango. Costruiamo poi la compattificazione wonderful dello spazio delle matrici simmetriche e simplettiche.
Grazie ad un risultato di D. Luna, le varietà wonderful sono varietà sferiche e quindi Mori dream spaces. Approfittando della struttura sferica di questi spazi studiamo la loro geometria birazionale dal punto di vista della teoria di Mori e nei casi di rango di Picard basso diamo una descrizione completa della decomposizione del cono effettivo.
Nella seconda parte mettiamo in relazione le nostre nuove compattificazioni wonderful con altri spazi di moduli come gli schemi di Hilbert e gli spazi di Kontsevich di mappe stabili. Infatti, otteniamo in questo modo molti risultati sulla geometria birazionale degli spazi di moduli di Kontsevich di coniche in Grassmanniane, in Grassmanniane Lagrangiane e di mappe stabili di bi-grado (1,1) in un prodotto di due spazi proiettivi.In this thesis we study certain algebraic varieties from the point of view of birational geometry. Given a variety we want to describe all its birational models. In general, this is a very difficult problem, but for a special class of varieties, called Mori dream spaces, the birational geometry is encoded in a decomposition into convex sets of their effective cone. Mori dream spaces have been introduced by Y. Hu and S. Keel, and are named so since they behave in the best possible way from the point of view of the minimal model program. The first part of the thesis is dedicated to the construction of wonderful compactifications of spaces of linear maps. We recall the construction, due to I. Vainsencher, of the spaces of complete collineations and quadrics of maximal rank and then we generalize it to spaces of linear maps of any rank. Then, we construct the wonderful compactification of the space of symmetric and symplectic matrices. By a result of D. Luna, wonderful varieties are spherical and hence Mori dream spaces. So, we take advantage of the spherical structure of these spaces to study their birational geometry from the point of view of Mori theory and in the cases of small Picard rank we give a complete description of the decomposition of the effective cone. In the second part, we relate our wonderful compactification to other moduli spaces such as Hilbert schemes and Kontsevich spaces of stable maps. In fact, we get several results on the birational geometry of Kontsevich moduli spaces of conics in Grassmannians, in Lagrangian Grassmannians and of stable maps of bi-degree (1,1) in a product of two projective spaces.
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Bergvall, Olof. "Cohomology of the moduli space of curves of genus three with level two structure." Licentiate thesis, Stockholms universitet, Matematiska institutionen, 2014. http://urn.kb.se/resolve?urn=urn:nbn:se:su:diva-103062.
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In this thesis we investigate the moduli space M3[2] of curves of genus 3 equipped with a symplectic level 2 structure. In particular, we are interested in the cohomology of this space. We obtain cohomological information by decomposing M3[2] into a disjoint union of two natural subspaces, Q[2] and H3[2], and then making S7- resp. S8-equivariantpoint counts of each of these spaces separately.Målet med denna uppsats är att undersöka modulirummet M3[2] av kurvor av genus 3 med symplektisk nivå 2 struktur. Mer specifikt vill vi hitta informationom kohomologin av detta rum. För att uppnå detta delar vi först upp M[2] i en disjunkt union av två naturliga delrum, Q[2] och H3[2], och räknar därefter punkterna av dessa rum S7- respektive S8-ekvivariant.
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Deopurkar, Anand. "Alternate Compactifications of Hurwitz Spaces." Thesis, Harvard University, 2012. http://dissertations.umi.com/gsas.harvard:10308.
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We construct several modular compactifications of the Hurwitz space \(H^d_{g/h}\) of genus g curves expressed as d-sheeted, simply branched covers of genus h curves. They are obtained by allowing the branch points of the cover to collide to a variable extent, generalizing the spaces of twisted admissible covers of Abramovich, Corti, and Vistoli. The resulting spaces are very well-behaved if d is small or if relatively few collisions are allowed. In particular, for d = 2 and 3, they are always well-behaved. For d = 2, we recover the spaces of hyperelliptic curves of Fedorchuk. For d = 3, we obtain new birational models of the space of triple covers. We describe in detail the birational geometry of the spaces of triple covers of \(P^1\) with a marked fiber. In this case, we obtain a sequence of birational models that begins with the space of marked (twisted) admissible covers and proceeds through the following transformations: (1) sequential contractions of the boundary divisors, (2) contraction of the hyperelliptic divisor, (3) sequential flips of the higher Maroni loci, (4) contraction of the Maroni divisor (for even g). The sequence culminates in a Fano variety in the case of even g, which we describe explicitly, and a variety fibered over \(P^1\) with Fano fibers in the case of odd g.Mathematics
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Dantas, Divane Aparecida de Moraes. "Espaço de moduli das configurações de desargues." Universidade Federal de Juiz de Fora, 2012. https://repositorio.ufjf.br/jspui/handle/ufjf/1781.
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O principal objetivo do trabalho é estudar os Espaços de Moduli das Configurações de Desargues, e este estudo é baseado no artigo (AVRITZER; LANGE, 2002). Uma configuração de 10 pontos e 10 retas, chamada uma configuração 103,obtidas do clássico teorema de Desargues, é chamada uma configuração de Desargues. Muitos espaços de moduli, senão todos, são obtidos algebricamente através das variedades algébricas de quociente, por isso estudamos um pouco de Teoria Geométrica dos Invariantes, ações de grupos algébricos em variedades algébricas e mostramos que existe o quociente categórico de uma variedade algébrica X por um grupo finito G e quando ele é o espaço e moduli grosso. Além disso mostramos que quando a variedade algébrica é afim (resp. quase projetiva) o quociente categórico é uma variedade algébrica afim (resp. quase projetiva). Finalmente, provamos que o quociente categórico(MD,p) de ˇP3 pelo grupo finito S5 é o espaço de moduli grosso para as configurações de Desargues.
The main aim of this work is to study the moduli space of Desargues configurations and it was based in (AVRITZER; LANGE, 2002). A configurations of 10 points and 10 line of the classic Desargues Theorem is called a Desargues configuration. Many moduli spaces, if not all, are obtained algebraically through the quotient of algebraic varieties. So we have studied a little about Geometric Invariant Theory and actions of algebraic group on varieties. We have showed that there exist the categorical quotient of a algebraic variety X by a finite algebraic group G and that it is a coarse moduli space. Moreover, we have showed that if X is a affine (resp. quasi-projective) the categorical quotient is an affine (resp. quasi-projective) variety Finally, we proved that the categorical quotient (MD,p) of the ˇP3 by the algebraic group finite S5 is the moduli space coarse for the Desargues configurations.
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Chen, Yifan Verfasser], and Fabrizio [Akademischer Betreuer] [Catanese. "Two Irreducible Components of the Moduli Space M can 1,3 / Yifan Chen. Betreuer: Fabrizio Catanese." Bayreuth : Universitätsbibliothek Bayreuth, 2012. http://d-nb.info/1020871121/34.
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Shao, Yijun. "A Compactification of the Space of Algebraic Maps from P^1 to a Grassmannian." Diss., The University of Arizona, 2010. http://hdl.handle.net/10150/194715.
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Let Md be the moduli space of algebraic maps (morphisms) of degree d from P^1 to a fixed Grassmannian. The main purpose of this thesis is to provide an explicit construction of a compactification of Md satisfying the following property: the compactification is a smooth projective variety and the boundary is a simple normal crossing divisor. The main tool of the construction is blowing-up. We start with a smooth compactification given by Quot scheme, which we denote by Qd. The boundary Qd\Md is singular and of high codimension. Next, we give a filtration of the boundary Qd\Md by closed subschemes: Zd,0 subset Zd,1 subset ... Zd,d-1=Qd\Md. Then we blow up the Quot scheme Qd along these subschemes succesively, and prove that the final outcome is a compactification satisfying the desired properties. The proof is based on the key observation that each Zd,r has a smooth projective variety which maps birationally onto it. This smooth projective variety, denoted by Qd,r, is a relative Quot scheme over the Quot-scheme compactification Qr for Mr. The map from Qd,r to Zd,r is an isomorphism when restricted to the preimage of Zd,r\ Zd,r-1. With the help of the Qd,r's, one can show that the final outcome of the successive blowing-up is a smooth compactification whose boundary is a simple normal crossing divisor.
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Takahashi, Ryosuke. "The Moduli Space of S1-Type Zero Loci for Z/2 Harmonic Spinors in Dimension 3." Thesis, Harvard University, 2015. http://nrs.harvard.edu/urn-3:HUL.InstRepos:17463144.
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Let M be a compact oriented 3-dimensional smooth manifold. In this paper, we will construct a moduli space consisting of the following date {(Σ,ψ)} where Σ is a C1-embedding S1 curve in M, ψ is a Z/2-harmonic spinor vanishing only on Σ and kψkL21 = 1. We will prove that this moduli space can be parametrized by the space X = { all Riemannian metrics on M } locally as the kernel of a Fredholm operator.Mathematics
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Marín, Pérez David. "Problemas de módulos para una clase de foliaciones holomorfas." Doctoral thesis, Universitat Autònoma de Barcelona, 2001. http://hdl.handle.net/10803/3067.
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Kadiköylü, Irfan. "Rank Stratification of Spaces of Quadrics and Moduli of Curves." Doctoral thesis, Humboldt-Universität zu Berlin, 2018. http://dx.doi.org/10.18452/19191.
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In dieser Arbeit untersuchen wir Varietäten singulärer, quadratischer Hyperflächen, die eine projektive Kurve enthalten, und effektive Divisoren im Modulraum von Kurven, die mittels verschiedener Eigenschaften von quadratischen Hyperflächen definiert werden.
In Kapitel 2 berechnen wir die Klasse des effektiven Divisors im Modulraum von Kurven mit Geschlecht g und n markierten Punkten, der als der Ort von solchen markierten Kurven definiert ist, dass das Projektion der kanonischen Abbildung der Kurve von den markierten Punkten auf einer quadratischen Hyperfläche liegt. Mithilfe dieser Klasse zeigen wir, dass die Modulräume mit Geschlecht 16, 17 und 8 markierten Punkten Varietäten von allgemeinem Typ sind.
In Kapitel 3 stratifizieren wir den Raum von quadratischen Hyperflächen, die eine projektive Kurve enthalten, mithilfe des Rangs dieser Hyperflächen. Wir zeigen, dass jedes Stratum die erwartete Dimension hat, falls die Kurve ein allgemeines Element des Hilbertschemas ist. Mit Rücksicht auf Rang von quadratischen Hyperflächen, eine ähnliche Konstruktion wie in Kapitel 2 ergibt neue Divisoren im Modulraum von Kurven. Wir berechnen die Klasse von diesen Divisoren und zeigen, dass der Modulraum von Kurven mit Geschlecht 15 und 9 markierten Punkten eine Varietät von allgemeinem Typ ist.
In Kapitel 4 präsentieren wir unterschiedliche Resultate, die mit Themen von vorigen Kapiteln im Zusammenhang stehen. Zum Ersten berechnen wir die Klasse von Divisoren im Modulraum von Kurven, die als die Orte von Kurven definiert sind, wo die maximale Rang Vermutung nicht gilt. Zweitens zeigen wir, dass jedes Geradenbündel als Tensorprodukt von zwei Geradenbündeln mit zwei Schnitten geschrieben werden kann, falls die Kurve allgemein ist und eine gewisse numerische Bedingung erfüllt ist. Zuletzt benutzen wir bekannte Divisorklassen zu zeigen, dass der Modulraum von Kurven mit Geschlecht 12 und 10 markierten Punkten eine Varietät von allgemeinem Typ ist.In this thesis, we study varieties of singular quadrics containing a projective curve and effective divisors in the moduli space of pointed curves defined via various constructions involving quadric hypersurfaces. In Chapter 2, we compute the class of the effective divisor in the moduli space of n-pointed genus g curves, which is defined as the locus of pointed curves such that the projection of the canonical model of the curve from the marked points lies on a quadric hypersurface. Using this class, we show that the moduli spaces of 8-pointed genus 16 and 17 curves are varieties of general type. In Chapter 3, we stratify the space of quadrics that contain a given curve in the projective space, using the ranks of the quadrics. We show, in a certain numerical range, that each stratum has the expected dimension if the curve is general in its Hilbert scheme. By incorporating the datum of the rank of quadrics, a similar construction as the one in Chapter 2 yields new divisors in the moduli space of pointed curves. We compute the class of these divisors and show that the moduli space of 9-pointed genus 15 curves is a variety of general type. In Chapter 4, we present miscellaneous results, which are related with our main work in the previous chapters. Firstly, we consider divisors in the moduli space of genus g curves, which are defined as the failure locus of maximal rank conjecture for hypersurfaces of degree greater than two. We illustrate three examples of such divisors and compute their classes. Secondly, using the classical correspondence between rank 4 quadrics and pencils on curves, we show that the map that associates to a pair of pencils their tensor product in the Picard variety is surjective, when the curve is general and obvious numerical assumptions are satisfied. Finally, we use divisor classes, that are already known in the literature, to show that the moduli space of 10-pointed genus 12 curves is a variety of general type.
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Tate, Dominic. "On the Fock-Goncharov Moduli Space for Real Projective Structures on Surfaces: Cell Decomposition, Buildings and Compactification." Thesis, The University of Sydney, 2020. https://hdl.handle.net/2123/22342.
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Let S be a non-compact surface with empty boundary and negative Euler characteristic. Fock and Goncharov [2006, 2007] devise coordinate systems for the space of properly convex projective structures on S and for the space of doubly-decorated finite-area projective structures on S. These are known as the spaces of X-coordinates and A-coordinates respectively. We use the former to provide straightforward proofs of known results regarding the moduli space of convex projective structures on surfaces of finite area, due to Marquis [2010], and closed surfaces, due to Goldman [1990]. The latter coordinate space is then shown to have a natural cell decomposition induced by the canonical cell decomposition of a real projective surface due to Cooper and Long [2015]. In the final chapter we recall Parreau's [2012] generalisation of Thurston's [1988] compactification of Teichmüller space via length spectra. Subsequently, Parreau [2015] provides a method of assigning an action of the fundamental group of S on a Euclidean building to points on the boundary of this compactified space as well as a fundamental group-invariant subset of the building for some such points. Parreau's construction depends upon a choice of ideal triangulation so a natural question to ask is whether or not for each point on the ideal boundary of the moduli space there exists an ideal triangulation with respect to which Parreau's construction provides a fundamental group-invariant subset of the building. We answer this question in the negative. We modify Parreau's construction to provide a fundamental group-invariant subset to a dense subset of the boundary points. Moreover this is done in a way that is independent of the choice of ideal triangulation used to define the X-coordinates.
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Zhou, Jie. "Arithmetic Properties of Moduli Spaces and Topological String Partition Functions of Some Calabi-Yau Threefolds." Thesis, Harvard University, 2014. http://dissertations.umi.com/gsas.harvard:11352.
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This thesis studies certain aspects of the global properties, including geometric and arithmetic, of the moduli spaces of complex structures of some special Calabi-Yau threefolds (B-model), and of the corresponding topological string partition functions defined from them which are closely related to the generating functions of Gromov-Witten invariants of their mirror Calabi-Yau threefolds (A-model) by the mirror symmetry conjecture.Mathematics
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Vizarreta, Eber Daniel Chuño. "Elementos da teoria de Teichmüller." Universidade de São Paulo, 2012. http://www.teses.usp.br/teses/disponiveis/55/55135/tde-20032012-103343/.
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Nesta disertação estudamos algumas ferramentas básicas relacionadas aos espaços de Teichmüller. Introduzimos o espaço de Teichmüller de gênero g ≥ 1, denotado por Tg. O objetivo principal é construir as coordenadas de Fenchel-Nielsen ωG : Tg → R3g-3+ × R3g-3 para cada grafo trivalente marcado G.In this dissertation we study some basic tools related to Teichmüller space. We introduce the Teichmüller space of genus g ≥ 1, denoted by Tg. The main goal is to construct the Fenchel-Nielsen coordinates ωG : Tg → R3g-3+ × R3g-3 to each marked cubic graph G.
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Liese, Carsten [Verfasser], and Bernd [Akademischer Betreuer] Siebert. "The KSBA compactification of the moduli space of degree 2 K3 pairs : a toroidal interpretation / Carsten Liese ; Betreuer: Bernd Siebert." Hamburg : Staats- und Universitätsbibliothek Hamburg, 2018. http://d-nb.info/1164158651/34.
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Liese, Carsten Verfasser], and Bernd [Akademischer Betreuer] [Siebert. "The KSBA compactification of the moduli space of degree 2 K3 pairs : a toroidal interpretation / Carsten Liese ; Betreuer: Bernd Siebert." Hamburg : Staats- und Universitätsbibliothek Hamburg, 2018. http://nbn-resolving.de/urn:nbn:de:gbv:18-92512.
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TAMBORINI, CAROLINA. "On totally geodesic subvarieties in the Torelli locus and their uniformizing symmetric spaces." Doctoral thesis, Università degli Studi di Milano-Bicocca, 2022. http://hdl.handle.net/10281/371476.
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Oggetto di questa tesi sono le sottovarietà totalmente geodetiche dello spazio dei moduli A_g di varietà abeliane principalmente polarizzate e la loro relazione con il luogo di Torelli. Questo è definito come la chiusura in A_g dell'immagine dello spazio dei moduli M_g di curve algebriche complesse lisce di genere g tramite la mappa di Torelli j: M_g-->A_g. Lo spazio dei moduli A_g è un quoziente dello spazio di Siegel, che è uno spazio simmetrico. Una sottovarietà algebrica di A_g è totalmente geodetica se è l'immagine, tramite la naturale mappa di proiezione, di una qualche sottovarietà totalmente geodetica dello spazio di Siegel. Ci si aspetta che j(M_g) contenga poche sottovarietà totalmente geodetiche di A_g. Questo è anche in accordo con la congettura di Coleman-Oort. La geometria differenziale degli spazi simmetrici si può descrivere attraverso la teoria di gruppi e algebre di Lie. In particolare, le sottovarietà totalmente geodetiche di spazi simmetrici possono essere caratterizzate in termini di algebre di Lie. Queste considerazioni sono alla base della trattazione svolta in questa tesi, in cui utilizziamo alcuni strumenti della teoria di Lie per indagare alcuni aspetti geometrici dell'inclusione di j(M_g) in A_g. I principali risultati presentati sono i seguenti. Nel Capitolo 2, consideriamo il pull-back dell'operazione di Lie-bracket sullo spazio tangente ad A_g tramite la mappa di Torelli e lo caratterizziamo in termini della geometria della curva. Per farlo usiamo il nucleo di Bergman associato alla curva. Inoltre, colleghiamo il nucleo di Bergman alla seconda forma fondamentale della mappa Torelli. Nel Capitolo 3, determiniamo quale spazio simmetrico uniforma ciascuno dei controesempi noti alla congettura di Coleman-Oort attraverso il calcolo della decomposizione dell'algebra di Lie associata. Questi esempi noti erano stati ottenuti studiando famiglie di rivestimenti di Galois. Nel capitolo 4 ci concentriamo sullo studio di queste famiglie e descriviamo una nuova costruzione topologica di famiglie di G-rivestimenti di P^1.This thesis deals with totally geodesic subvarieties of the moduli space A_g of principally polarized abelian varieties and their relation with the Torelli locus. This is the closure in A_g of the image of the moduli space M_g of smooth, complex algebraic curves of genus g via the Torelli map j: M_g-->A_g. The moduli space A_g is a quotient of the Siegel space, which is a Riemannian symmetric space. An algebraic subvariety of A_g is totally geodesic if it is the image, under the natural projection map, of some totally geodesic submanifold of the Siegel space. Geometric considerations lead to the expectation that j(M_g) should contain very few totally geodesic subvarieties of A_g. This expectation also agrees with the Coleman-Oort conjecture. The differential geometry of symmetric spaces is described through Lie theory. In particular, totally geodesic submanifolds can be characterized via Lie algebras. This motivates the discussion carried out in this thesis, in which we use some Lie-theoretic tools to investigate geometric aspects of the inclusion of j(M_g) in A_g. The main results presented are the following. In Chapter 2, we consider the pull-back of the Lie bracket operation on the tangent space of A_g via the Torelli map, and we characterize it in terms of the geometry of the curve. We use the Bergman kernel form associated with the curve. Also, we link the Bergman kernel form to the second fundamental form of the Torelli map. In Chapter 3, we determine which symmetric space uniformizes each of the known counterexamples to the Coleman-Oort conjecture via the computation of the associated Lie algebra decomposition. These known examples were obtained studying families of Galois coverings of curves. Chapter 4 focuses on these families for their own sake, and we describe a new topological construction of families of G-coverings of the line.
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Larsen, Paul L. [Verfasser], Klaus [Akademischer Betreuer] Altmann, Gavril [Akademischer Betreuer] Farkas, and Angela [Akademischer Betreuer] Gibney. "Applied Mori theory of the moduli space of stable pointed rational curves / Paul L. Larsen. Gutachter: Klaus Altmann ; Gavril Farkas ; Angela Gibney." Berlin : Humboldt Universität zu Berlin, Mathematisch-Naturwissenschaftliche Fakultät II, 2011. http://d-nb.info/1015081487/34.
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Sciarappa, Antonio. "Developments in Quantum Cohomology and Quantum Integrable Hydrodynamics via Supersymmetric Gauge Theories." Doctoral thesis, SISSA, 2015. http://hdl.handle.net/20.500.11767/4867.
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Daniel, Panizo. "Review of compact spaces for type IIA/IIB theories and generalised fluxes." Thesis, Uppsala universitet, Institutionen för fysik och astronomi, 2019. http://urn.kb.se/resolve?urn=urn:nbn:se:uu:diva-384227.
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In the present project we study compactifications of type IIA/IIB string theories on toroidal orbifolds. We present the moduli space for N=1 four-dimensional reductions and its topological properties. To fix the value of all moduli, we will construct the most general holomorphic superpotential W using a set of T-dual iterations for the fluxes. Using a 3-torus toy-model, we will give an introductory description to the background of these generalised fluxes.