Relevant bibliographies by topics / Algebraic Geometry, Moduli spaces, Vector bundles

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  1. Journal articles
  2. Dissertations / Theses
  3. Books
  4. Book chapters

Academic literature on the topic 'Algebraic Geometry, Moduli spaces, Vector bundles'

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Published: 14 March 2023

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Journal articles on the topic "Algebraic Geometry, Moduli spaces, Vector bundles"

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Bhosle, Usha N. "Moduli spaces of vector bundles on a real nodal curve." Beiträge zur Algebra und Geometrie / Contributions to Algebra and Geometry 61, no. 4 (February 19, 2020): 615–26. http://dx.doi.org/10.1007/s13366-020-00489-5.

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BRADLOW, S. B., O. GARCÍA-PRADA, V. MERCAT, V. MUÑOZ, and P. E. NEWSTEAD. "ON THE GEOMETRY OF MODULI SPACES OF COHERENT SYSTEMS ON ALGEBRAIC CURVES." International Journal of Mathematics 18, no. 04 (April 2007): 411–53. http://dx.doi.org/10.1142/s0129167x07004151.

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Let C be an algebraic curve of genus g ≥ 2. A coherent system on C consists of a pair (E,V), where E is an algebraic vector bundle over C of rank n and degree d and V is a subspace of dimension k of the space of sections of E. The stability of the coherent system depends on a parameter α. We study the geometry of the moduli space of coherent systems for different values of α when k ≤ n and the variation of the moduli spaces when we vary α. As a consequence, for sufficiently large α, we compute the Picard groups and the first and second homotopy groups of the moduli spaces of coherent systems in almost all cases, describe the moduli space for the case k = n - 1 explicitly, and give the Poincaré polynomials for the case k = n - 2. In an appendix, we describe the geometry of the "flips" which take place at critical values of α in the simplest case, and include a proof of the existence of universal families of coherent systems when GCD (n,d,k) = 1.
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Lakshmibai, V., K. N. Raghavan, P. Sankaran, and P. Shukla. "Standard monomial bases, Moduli spaces of vector bundles, and Invariant theory." Transformation Groups 11, no. 4 (October 21, 2006): 673–704. http://dx.doi.org/10.1007/s00031-005-1123-4.

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Spies, Alexander. "Poisson-geometric Analogues of Kitaev Models." Communications in Mathematical Physics 383, no. 1 (March 9, 2021): 345–400. http://dx.doi.org/10.1007/s00220-021-03992-5.

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AbstractWe define Poisson-geometric analogues of Kitaev’s lattice models. They are obtained from a Kitaev model on an embedded graph $$\Gamma $$ Γ by replacing its Hopf algebraic data with Poisson data for a Poisson-Lie group G. Each edge is assigned a copy of the Heisenberg double $${\mathcal {H}}(G)$$ H ( G ) . Each vertex (face) of $$\Gamma $$ Γ defines a Poisson action of G (of $$G^*$$ G ∗ ) on the product of these Heisenberg doubles. The actions for a vertex and adjacent face form a Poisson action of the double Poisson-Lie group D(G). We define Poisson counterparts of vertex and face operators and relate them via the Poisson bracket to the vector fields generating the actions of D(G). We construct an isomorphism of Poisson D(G)-spaces between this Poisson-geometrical Kitaev model and Fock and Rosly’s Poisson structure for the graph $$\Gamma $$ Γ and the Poisson-Lie group D(G). This decouples the latter and represents it as a product of Heisenberg doubles. It also relates the Poisson-geometrical Kitaev model to the symplectic structure on the moduli space of flat D(G)-bundles on an oriented surface with boundary constructed from $$\Gamma $$ Γ .
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Aprodu, Marian, and Vasile Brînzănescu. "Moduli spaces of vector bundles over ruled surfaces." Nagoya Mathematical Journal 154 (1999): 111–22. http://dx.doi.org/10.1017/s0027763000025332.

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AbstractWe study moduli spaces M(c1, c2, d, r) of isomorphism classes of algebraic 2-vector bundles with fixed numerical invariants c1, c2, d, r over a ruled surface. These moduli spaces are independent of any ample line bundle on the surface. The main result gives necessary and sufficient conditions for the non-emptiness of the space M(c1, c2, d, r) and we apply this result to the moduli spaces ML(c1, c2) of stable bundles, where L is an ample line bundle on the ruled surface.
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Bochnak, J., W. Kucharz, and R. Silhol. "Morphisms, line bundles and moduli spaces in real algebraic geometry." Publications mathématiques de l'IHÉS 86, no. 1 (December 1997): 5–65. http://dx.doi.org/10.1007/bf02698900.

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Bochnak, Jacek, Wojciech Kucharz, and Robert Silhol. "Morphisms, line bundles and moduli spaces in real algebraic geometry." Publications mathématiques de l'IHÉS 92, no. 1 (December 2000): 195. http://dx.doi.org/10.1007/bf02698917.

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BOLOGNESI, MICHELE, and SONIA BRIVIO. "COHERENT SYSTEMS AND MODULAR SUBAVRIETIES OF $\mathcal{SU}_C(r)$." International Journal of Mathematics 23, no. 04 (April 2012): 1250037. http://dx.doi.org/10.1142/s0129167x12500371.

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Let C be an algebraic smooth complex curve of genus g > 1. The object of this paper is the study of the birational structure of certain moduli spaces of vector bundles and of coherent systems on C and the comparison of different type of notions of stability arising in moduli theory. Notably we show that in certain cases these moduli spaces are birationally equivalent to fibrations over simple projective varieties, whose fibers are GIT quotients (ℙr-1)rg// PGL (r), where r is the rank of the considered vector bundles. This allows us to compare different definitions of (semi-)stability (slope stability, α-stability, GIT stability) for vector bundles, coherent systems and point sets, and derive relations between them. In certain cases of vector bundles of low rank when C has small genus, our construction produces families of classical modular varieties contained in the Coble hypersurfaces.
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Schaffhauser, Florent. "Moduli spaces of vector bundles over a Klein surface." Geometriae Dedicata 151, no. 1 (August 1, 2010): 187–206. http://dx.doi.org/10.1007/s10711-010-9526-3.

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Serman, Olivier. "Moduli spaces of orthogonal and symplectic bundles over an algebraic curve." Compositio Mathematica 144, no. 3 (May 2008): 721–33. http://dx.doi.org/10.1112/s0010437x07003247.

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AbstractWe prove that, given a smooth projective curve C of genus g≥2, the forgetful morphism $\mathcal {M}_{\mathbf {O}_r} \longrightarrow \mathcal {M}_{\mathbf {GL}_r}$ (respectively $\mathcal M_{\mathbf {Sp}_{2r}}\longrightarrow \mathcal M_{\mathbf {GL}_{2r}}$) from the moduli space of orthogonal (respectively symplectic) bundles to the moduli space of all vector bundles over C is an embedding. Our proof relies on an explicit description of a set of generators for the polynomial invariants on the representation space of a quiver under the action of a product of classical groups.
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Dissertations / Theses on the topic "Algebraic Geometry, Moduli spaces, Vector bundles"

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Costa, Farràs Laura. "Moduli spaces of vector bundles on algebraic varieties." Doctoral thesis, Universitat de Barcelona, 1998. http://hdl.handle.net/10803/659.

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This thesis seeks to contribute to a deeper understanding of the moduli spaces M-sub X, H (r; c1,., Cmin{r;n}) of rank r, H-stable vector bundles E on an n-dimensional variety X, with fixed Chern classes c-sub1(E) = csub1 H-super2i ( X , Z) , displaying new and interesting geometric properties of M-sub X, H (r; c1,., Cmin{r;n}) which nicely reflect the general philosophy that moduli spaces inherit a lot of .geometrical properties of the underlying variety X.

More precisely, we consider a smooth, irreducible, n-dimensional, projective variety X defined over an algebraically closed field k of characteristic zero, H an ample divisor on X, r >/2 an integer and c-subi H-super2i(X,Z) for i = 1, .,min{r,n}. We denote by M-sub X, H (r; c1,., Cmin{r;n}) the moduli space of rank r, vector bundles E on X, H-stable, in the sense of Mumford-Takemoto, with fixed Chern classes c-subi(E) = c-subi for i = 1, . , min{r, n}.

The contents of this Thesis is the following: Chapter 1 is devoted to provide the reader with the general background that we will need in the sequel. In the first two sections, we have collected the main definitions and results concerning coherent sheaves and moduli spaces, at least, those we will need through this work.

The aim of Chapter 2 is to establish the enterions of rationality for moduli spaces of rank two, it-stable vector bundles on a smooth, irreducible, rational surface X that will be used as one of our tools for answering Question (1), who is that follows: "Let X be a smooth, irreducible, rational surface. Fix C-sub1 Pic(X) and 0 « c2 Z. Is there an ample divisor H on X such that M-sub X,H(2; Ci, c2) is rational?"

In Chapter 3 we prove that the moduli space M-sub X,H(2; Ci, c2) of rank two, H-stable, vector bundles E on a smooth, irreducible, rational surface X, with fixed Chern classes C-sub1(E) = C-sub1 Pic(X) and 0 « C-sub2«(E) Z is a smooth, irreducible, rational, quasi-projective variety (Theorem 3.3.7) which solves Question (1).

In Chapter 4 we study moduli spaces (M-sub X,H(2; Ci, c2)) of rank r, H-stable vector bundles on either minimal rational surfaces or on algebraic K3 surfaces.

In Chapter 5 we deal with moduli spaces M-sub x,l (2;Ci,C2) of rank two, L-stable vector bundles E, on P-bundles of arbitrary dimension, with fixed Chern classes.
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Lo, Giudice Alessio. "Some topics on Higgs bundles over projective varieties and their moduli spaces." Doctoral thesis, SISSA, 2013. http://hdl.handle.net/20.500.11767/4100.

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In this thesis we study vector bundles on projective varieties and their moduli spaces. In Chapters 2, 3 and 4 we recall some basic notions as Higgs bundles, decorated bundles and generalized parabolic sheaves and introduce the problem we want to study. In chapter 5, we study Higgs bundles on nodal curves. After moving the problem on the normalization of the curve, starting from a Higgs bundle we obtain a generalized parabolic Higgs bundle. Using decorated bundles we are able to construct a projective moduli space which parametrizes equivalence classes of Higgs bundles on a nodal curve X. This chapter is an extract of a joint work with Andrea Pustetto Later on Chapter 6 is devoted to the study of holomorphic pairs (or twisted Higgs bundles) on elliptic curve. Holomorphic pairs were introduced by Nitsure and they are a natural generalization of the concept of Higgs bundles. In this Chapter we extend a result of E. Franco, O. Garc\'ia-Prada And P.E. Newstead valid for Higgs bundles to holomorphic pairs. Finally the last Chapter describes a joint work with Professor Ugo Bruzzo. We study Higgs bundles over varieties with nef tangent bundle. In particular generalizing a result of Nitsure we prove that if a Higgs bundle $(E,\phi)$ over the variety X with nef tangent remains semisatble when pulled-back to any smooth curve then it discrimiant vanishes.
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Gronow, Michael Justin. "Extension maps and the moduli spaces of rank 2 vector bundles over an algebraic curve." Thesis, Durham University, 1997. http://etheses.dur.ac.uk/5081/.

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Let SUc(2,Ʌ) be the moduli space of rank 2 vector bundles with determinant Ʌ on an algebraic curve C. This thesis investigates the properties of a rational map PU(_d,A) →(^c,d) SUc(2, A) where PU(_d,A) is a projective bundle of extensions over the Jacobian J(^d)(C). In doing so the degree of the moduli space SUc(2, Oc) is calculated for non- hyperelliptic curves of genus four (3.4.2). Information about trisecants to the Kummer variety K C SUc(2,Oc) is obtained in sections 4.3 and 4.4. These sections describe the varieties swept out by these trisecants in the fibres of PU1,o(_c) → J(^1)(C) for curves of genus 3, 4 and 5. The fibres of over ϵ(_d) over E ϵ SUc{2,A) are then studied. For certain values of d these correspond to the family of maximal line subbundles of E. These are either zero or one dimensional and a complete description of when these families are smooth is given (5.4.9), (5.4.10). In the one dimensional case its genus is also calculated (if connected) (5.5.5). Finally a correspondence on the curve fibres is shown to exist (5.6.2) and its degree is calculated (5.6.5). This in turn gives some information about multisecants to projective curves (5.7.4), (5.7.7).
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Galeotti, Mattia Francesco. "Moduli of curves with principal and spin bundles : singularities and global geometry." Thesis, Paris 6, 2017. http://www.theses.fr/2017PA066485/document.

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L'espace de modules Mgbar des courbes stables de genre g est un object central en géométrie algébrique. Du point de vue de la géométrie birationelle, il apparaît naturel se demander si Mgbar est de type générale. Harris-Mumford et Eisenbud-Harris ont montré que Mgbar est de type générale pour un genre g>=24 et g=22. Le cas g=23 est encore misterieux. Dans les dix dernières années une nouvelle approche a émergé, dans l'essai de clarifier ça : l'idée est celle de considérer de recouvrement fini de Mgbar qui sont des espaces de modules de courbes stables munies d'une structure additionnelle comme un l-recouvrement (racine l-ième du fibré trivial) ou un fibré l-spin (racine l-ième du fibré canonique). Ces espaces ont la propriété que la transition au type générale se produit à un genre inférieur. Dans ce travail nous voulons généraliser cette approche de deux façons : - un étude de l'espace de modules des courbes avec une racine d'une puissance quelconque du fibré canonique ; - un étude de l'espace de modules des courbes avec un G-recouvrement pour un quelconque G groupe fini. Pour définir ces espaces de modules nous utilisons la notion de courbe twisted (voir Abramovich-Corti-Vistoli). Le résultat fondamental obtenu est qu'il est possible de décrire le lieu singulier de ces espaces de modules par la notion de graphe dual d'une courbe. Grace à cette analyse, nous pouvons developper des calculs dans l'anneau tautologique des espaces, et en particulier nous conjecturons que l'espace de modules des courbes avec un S3-recouvrement est de type générale pour genre impaire g>=13
The moduli space Mgbar of genus g stable curves is a central object in algebraic geometry. From the point of view of birational geometry, it is natural to ask if Mgbar is of general type. Harris-Mumford and Eisenbud-Harris found that Mgbar is of general type for genus g>=24 and g=22. The case g=23 keep being mysterious. In the last decade, in an attempt to clarify this, a new approach emerged: the idea is to consider finite covers of Mgbar that are moduli spaces of stable curves equipped with additional structure as l-covers (l-th roots of the trivial bundle) or l-spin bundles (l-th roots of the canonical bundle). These spaces have the property that the transition to general type happens to a lower genus. In this work we intend to generalize this approach in two ways: - a study of moduli space of curves with any root of any power of the canonical bundle; - a study of the moduli space of curves with G-covers for any finite group G. In order to define these moduli spaces we use the notion of twisted curve (see Abramovich-Corti-Vistoli). The fundamental result obtained is that it is possible to describe the singular locus of these moduli spaces via the notion of dual graph of a curve. Thanks to this analysis, we are able to develop calculations on the tautological rings of the spaces, and in particular we conjecture that the moduli space of curves with S3-covers is of general type for odd genus g>=13
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Schlüeter, Dirk Christopher. "Universal moduli of parabolic sheaves on stable marked curves." Thesis, University of Oxford, 2011. http://ora.ox.ac.uk/objects/uuid:b0260f8e-6654-4bec-b670-5e925fd403dd.

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The topic of this thesis is the moduli theory of (parabolic) sheaves on stable curves. Using geometric invariant theory (GIT), universal moduli spaces of semistable parabolic sheaves on stable marked curves are constructed: `universal' indicates that these are moduli spaces of pairs where the underlying marked curve may vary as well as the parabolic sheaf (as in the Pandharipande moduli space for pairs of stable curves and torsion-free sheaves without augmentations). As an intermediate step in this construction, we construct moduli spaces of semistable parabolic sheaves on flat families of arbitrary projective schemes (of any dimension or singularity type): this is the technical core of this thesis. These moduli spaces are projective, since they are constructed as GIT quotients of projective parameter spaces. The stability condition for parabolic sheaves depends on a choice of polarisation and is derived from the Hilbert-Mumford criterion. It is not quite the same as traditional stability with respect to parabolic Hilbert polynomials, but it is closely related to it, and the resulting moduli spaces are always compactifications of moduli of slope-stable parabolic sheaves. The construction works over algebraically closed fields of arbitrary characteristic.
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Prata, Daniela Moura 1984. "Representations of quivers and vector bundles over projectives spaces = Representações de quivers e fibrados vetoriais sobre espaços projetivos." [s.n.], 2012. http://repositorio.unicamp.br/jspui/handle/REPOSIP/306012.

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Orientador: Marcos Benevenuto Jardim
Tese (doutorado) - Universidade Estadual de Campinas, Instituto de Matemática, Estatística e Computação Científica
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Fernández, Vargas Néstor. "Fibres vectoriels sur des courbes hyperelliptiques." Thesis, Rennes 1, 2018. http://www.theses.fr/2018REN1S051/document.

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Cette thèse est dédiée à l'étude des espaces de modules de fibrés sur une courbe algébrique et lisse sur le corps des nombres complexes. Le texte est composé de deux parties : Dans la première partie, je m'intéresse à la géométrie liée aux classifications de fibrés quasi-paraboliques de rang 2 sur une courbe elliptique 2-pointée, à isomorphisme près. Les notions d'indécomposabilité, simplicité et stabilité de fibrés donnent lieu à des espaces de modules qui classifient ces objets. La structure projective de ces espaces est décrite explicitement, et on prouve un théorème de type Torelli qui permet de retrouver la courbe elliptique 2-pointée. Cet espace de modules est aussi mis en relation avec l'espace de modules de fibrés quasi-paraboliques sur une courbe rationnelle 5-pointée, qui apparaît naturellement comme revêtement double de l'espace de modules de fibrés quasi-paraboliques sur la courbe elliptique 2-pointée. Finalement, on démontre explicitement la modularité des automorphismes de cet espace de modules. Dans la deuxième partie, j'étudie l'espace de modules de fibrés semistables de rang 2 et déterminant trivial sur une courbe hyperelliptique. Plus précisément, je m'intéresse à l'application naturelle donnée par le fibré déterminant, générateur du groupe de Picard de cet espace de modules. Cette application s'identifie à l'application theta, qui est de degré 2 dans notre cas. On définit une fibration de cet espace de modules vers un espace projective dont la fibre générique est birationnelle à l'espace de modules de courbes rationnelles 2g-épointées, et on décrit la restriction de theta aux fibres de cette fibration. On montre que cette restriction est, à une transformation birationnelle près, une projection osculatoire centrée en un point. En utilisant une description due à Kumar, on démontre que la restriction de l'application theta à cette fibration ramifie sur la variété de Kummer d'une certaine courbe hyperelliptique de genre g – 1
This thesis is devoted to the study of moduli spaces of vector bundles over a smooth algebraic curve over field of complex numbers. The text consist of two main parts : In the first part, I investigate the geometry related to the classifications of rank 2 quasi-parabolic vector bundles over a 2-pointed elliptic curves, modulo isomorphism. The notions of indecomposability, simplicity and stability give rise to the corresponding moduli spaces classifying these objects. The projective structure of these spaces is explicitely described, and we prove a Torelli theorem that allow us to recover the 2-pointed elliptic curve. I also explore the relation with the moduli space of quasi-parabolic vector bundles over a 5-pointed rational curve, appearing naturally as a double cover of the moduli space of quasi-parabolic vector bundles over the 2-pointed elliptic curve. Finally, we show explicitely the modularity of the automorphisms of this moduli space. In the second part, I study the moduli space of semistable rank 2 vector bundles with trivial determinant over a hyperelliptic curve C. More precisely, I am interested in the natural map induced by the determinant line bundle, generator of the Picard group of this moduli space. This map is identified with the theta map, which is of degree 2 in our case. We define a fibration from this moduli space to a projective space whose generic fiber is birational to the moduli space of 2g-pointed rational curves, and we describe the restriction of the map theta to the fibers of this fibration. We show that this restriction is, up to a birational map, an osculating projection centered on a point. By using a description due to Kumar, we show that the restriction of the map theta to this fibration ramifies over the Kummer variety of a certain hyperelliptic curve of genus g - 1
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Benedetti, Vladimiro. "Sous-variétés spéciales des espaces homogènes." Thesis, Aix-Marseille, 2018. http://www.theses.fr/2018AIXM0224/document.

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Le but de cette thèse est de construire de nouvelles variétés algébriques complexes de Fano et à canonique triviale dans les espaces homogènes et d'analyser leur géométrie. On commence en construisant les variétés spéciales comme lieux de zéros de fibrés homogènes dans les grassmanniennes généralisées. On donne une complète classification en dimension 4. On prouve que les uniques variétés de dimension 4 hyper-Kahleriennes ainsi construites sont les exemples de Beauville-Donagi et Debarre-Voisin. Le même résultat vaut dans les grassmanniennes ordinaires en toute dimension quand le fibré est irréductible. Ensuite on utilise les lieux de dégénérescence orbitaux (ODL), qui généralisent les lieux de dégénérescence classiques, pour construire d'autres variétés. On rappelle les propriétés basiques des ODL, qu'on définit à partir d'une adhérence d'orbite. On construit trois schémas de Hilbert de deux points sur une K3 comme ODL, et beaucoup d'autres exemples de variétés de Calabi-Yau et de Fano. Puis on étudie les adhérences d'orbites dans les représentations de carquois, et on décrit des effondrements de Kempf pour celles de type A_n et D_4; ceci nous permet de construire davantage de variétés spéciales comme ODL. Pour finir, on analyse les grassmanniennes bisymplectiques, qui sont des Fano particulières. Elles admettent l'action d'un tore avec un nombre fini de points fixes. On étudie leurs petites déformations. Ensuite, on étudie la cohomologie (équivariante) des grassmanniennes symplectiques, qui est utile pour mieux comprendre la cohomologie des grassmanniennes bisymplectiques. On analyse en détail un cas explicite en dimension 6
The aim of this thesis is to construct new interesting complex algebraic Fano varieties and varieties with trivial canonical bundle and to analyze their geometry. In the first part we construct special varieties as zero loci of homogeneous bundles inside generalized Grassmannians. We give a complete classification for varieties of small dimension when the bundle is completely reducible. Thus, we prove that the only fourfolds with trivial canonical bundle so constructed which are hyper-Kahler are the examples of Beauville-Donagi and Debarre-Voisin. The same holds in ordinary Grassmannians when the bundle is irreducible in any dimension. In the second part we use orbital degeneracy loci (ODL), which are a generalization of classical degeneracy loci, to construct new varieties. ODL are constructed from a model, which is usually an orbit closure inside a representation. We recall the fundamental properties of ODL. As an illustration of the construction, we construct three Hilbert schemes of two points on a K3 surface as ODL, and many examples of Calabi-Yau and Fano threefolds and fourfolds. Then we study orbit closures inside quiver representations, and we provide crepant Kempf collapsings for those of type A_n, D_4; this allows us to construct some special varieties as ODL.Finally we focus on a particular class of Fano varieties, namely bisymplectic Grassmannians. These varieties admit the action of a torus with a finite number of fixed points. We find the dimension of their moduli space. We then study the equivariant cohomology of symplectic Grassmannians, which turns out to help understanding better that of bisymplectic ones. We analyze in detail the case of dimension 6
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Spinaci, Marco. "Déformations des applications harmoniques tordues." Phd thesis, Grenoble, 2013. http://tel.archives-ouvertes.fr/tel-00877310.

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On étudie les déformations des applications harmoniques $f$ tordues par rapport à une représentation. Après avoir construit une application harmonique tordue "universelle", on donne une construction de toute déformations du premier ordre de $f$ en termes de la théorie de Hodge ; on applique ce résultat à l'espace de modules des représentations réductives d'un groupe de Kähler, pour démontrer que les points critiques de la fonctionnelle de l'énergie $E$ coïncident avec les représentations de monodromie des variations complexes de structures de Hodge. Ensuite, on procède aux déformations du second ordre, où des obstructions surviennent ; on enquête sur l'existence de ces déformations et on donne une méthode pour les construire. En appliquant ce résultat à la fonctionnelle de l'énergie comme ci-dessus, on démontre (pour n'importe quel groupe de présentation finie) que la fonctionnelle de l'énergie est strictement pluri sous-harmonique sur l'espace des modules des représentations. En assumant de plus que le groupe soit de Kähler, on étudie les valeurs propres de la matrice hessienne de $E$ aux points critiques.
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Nevins, Thomas A. "Moduli spaces of framed sheaves on ruled surfaces /." 2000. http://gateway.proquest.com/openurl?url_ver=Z39.88-2004&res_dat=xri:pqdiss&rft_val_fmt=info:ofi/fmt:kev:mtx:dissertation&rft_dat=xri:pqdiss:9965126.

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Books on the topic "Algebraic Geometry, Moduli spaces, Vector bundles"

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1957-, Bradlow Steve, ed. Moduli spaces and vector bundles. Cambridge: Cambridge University Press, 2009.

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Compact moduli spaces and vector bundles: Conference on compact moduli and vector bundles, October 21-24, 2010, University of Georgia, Athens, Georgia. Providence, R.I: American Mathematical Society, 2012.

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Clay Mathematics Institute Workshop on Moduli Spaces of Vector Bundles, with a View toward Coherent Sheaves (2006 Cambridge, Mass.). Grassmannians, moduli spaces, and vector bundles: Clay Mathematics Institute Workshop on Moduli Spaces of Vector Bundles, with a View towards Coherent Sheaves, October 6-11, 2006, Cambridge, Massachusetts. Edited by Ellwood D. (David) 1966- and Previato Emma. Providence, RI: American Mathematical Society, 2011.

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1776-1853, Hoene-Wroński Józef Maria, and Pragacz Piotr, eds. Algebraic cycles, sheaves, shtukas, and moduli. Basel: Birkhäuser, 2008.

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Moduli spaces and arithmetic dynamics. Providence, R.I: American Mathematical Society, 2012.

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Schneider, Michael, 1942 May 18- and Spindler Heinz 1947-, eds. Vector bundles on complex projective spaces. [New York]: Springer, 2011.

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Luke, Glenys. Vector Bundles and Their Applications. Boston, MA: Springer US, 1998.

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1960-, García-Prada O. (Oscar), ed. Vector bundles and complex geometry: Conference on vector bundles in honor of S. Ramanan on the occasion of his 70th birthday, June 16-20, 2008, Miraflores de la Sierra, Madrid, Spain. Providence, R.I: American Mathematical Society, 2010.

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Moduli spaces of Riemann surfaces. Providence, Rhode Island: American Mathematical Society, 2013.

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Klaus, Hulek, ed. Complex algebraic varieties: Proceedings of a conference held in Bayreuth, Germany, April 2-6, 1990. Berlin: Springer-Verlag, 1992.

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Book chapters on the topic "Algebraic Geometry, Moduli spaces, Vector bundles"

1

Maruyama, Masaki. "Stable rationality of some moduli spaces of vector bundles on P2." In Complex Analysis and Algebraic Geometry, 80–89. Berlin, Heidelberg: Springer Berlin Heidelberg, 1986. http://dx.doi.org/10.1007/bfb0076996.

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Li, Jun. "The Geometry of Moduli Spaces of Vector Bundles over Algebraic Surfaces." In Proceedings of the International Congress of Mathematicians, 508–16. Basel: Birkhäuser Basel, 1995. http://dx.doi.org/10.1007/978-3-0348-9078-6_44.

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Tyurin, A. N. "The geometry of the special components of moduli space of vector bundles over algebraic surfaces of general type." In Lecture Notes in Mathematics, 166–75. Berlin, Heidelberg: Springer Berlin Heidelberg, 1992. http://dx.doi.org/10.1007/bfb0094518.

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Jost, Jürgen, and Xiao-Wei Peng. "The geometry of moduli spaces of stable vector bundles over riemann surfaces." In Global Differential Geometry and Global Analysis, 79–96. Berlin, Heidelberg: Springer Berlin Heidelberg, 1991. http://dx.doi.org/10.1007/bfb0083631.

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Maurin, Krzysztof. "Differential Geometry of Holomorphic Vector Bundles over Compact Riemann Surfaces and Kähler manifolds. Stable Vector Bundles, Hermite-Einstein Connections, and their Moduli Spaces." In The Riemann Legacy, 615–47. Dordrecht: Springer Netherlands, 1997. http://dx.doi.org/10.1007/978-94-015-8939-0_54.

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Balaji, V., and P. A. Vishwanath. "On the deformation theory of moduli spaces of vector bundles." In Vector Bundles in Algebraic Geometry, 1–14. Cambridge University Press, 1995. http://dx.doi.org/10.1017/cbo9780511569319.002.

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Drézet, J. M. "Exceptional bundles and moduli spaces of stable sheaves on ℙn." In Vector Bundles in Algebraic Geometry, 101–18. Cambridge University Press, 1995. http://dx.doi.org/10.1017/cbo9780511569319.005.

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Hu, Wenyao, and Xiaotao Sun. "Moduli Spaces of Vector Bundles on a Nodal Curve." In Forty Years of Algebraic Groups, Algebraic Geometry, and Representation Theory in China, 241–83. WORLD SCIENTIFIC, 2022. http://dx.doi.org/10.1142/9789811263491_0014.

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MARUYAMA, Masaki. "On a Compactification of a Moduli Space of Stable Vector Bundles on a Rational Surface." In Algebraic Geometry and Commutative Algebra, 233–60. Elsevier, 1988. http://dx.doi.org/10.1016/b978-0-12-348031-6.50020-6.

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"Chapter VII. Moduli spaces of vector bundles." In Differential Geometry of Complex Vector Bundles, 237–90. Princeton University Press, 1987. http://dx.doi.org/10.1515/9781400858682.237.

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