Relevant bibliographies by topics / Moduli space of vector bundles

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

Academic literature on the topic 'Moduli space of vector bundles'

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Published: 14 March 2023

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Journal articles on the topic "Moduli space of vector bundles"

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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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Beck, N. "Moduli of decorated swamps on a smooth projective curve." International Journal of Mathematics 26, no. 10 (September 2015): 1550086. http://dx.doi.org/10.1142/s0129167x1550086x.

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In order to unify the construction of the moduli space of vector bundles with different types of global decorations, such as Higgs bundles, framed vector bundles and conic bundles, A. H. W. Schmitt introduced the concept of a swamp. In this work, we consider vector bundles with both a global and a local decoration over a fixed point of the base. This generalizes the notion of parabolic vector bundles, vector bundles with a level structure and parabolic Higgs bundles. We introduce a notion of stability and construct the coarse moduli space for these objects as the GIT-quotient of a parameter space. In the case of parabolic vector bundles and vector bundles with a level structure our stability concept reproduces the known ones. Thus, our work unifies the construction of their moduli spaces.
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Basu, Suratno, and Sourav Das. "A Torelli type theorem for nodal curves." International Journal of Mathematics 32, no. 07 (April 23, 2021): 2150041. http://dx.doi.org/10.1142/s0129167x21500415.

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The moduli space of Gieseker vector bundles is a compactification of moduli of vector bundles on a nodal curve. This moduli space has only normal-crossing singularities and it provides flat degeneration of the moduli of vector bundles over a smooth projective curve. We prove a Torelli type theorem for a nodal curve using the moduli space of stable Gieseker vector bundles of fixed rank (strictly greater than [Formula: see text]) and fixed degree such that rank and degree are co-prime.
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Almeida, C., M. Jardim, A. S. Tikhomirov, and S. A. Tikhomirov. "New moduli components of rank 2 bundles on projective space." Sbornik: Mathematics 212, no. 11 (November 1, 2021): 1503–52. http://dx.doi.org/10.1070/sm9490.

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Abstract We present a new family of monads whose cohomology is a stable rank 2 vector bundle on . We also study the irreducibility and smoothness together with a geometrical description of some of these families. These facts are used to construct a new infinite series of rational moduli components of stable rank 2 vector bundles with trivial determinant and growing second Chern class. We also prove that the moduli space of stable rank 2 vector bundles with trivial determinant and second Chern class equal to 5 has exactly three irreducible rational components. Bibliography: 40 titles.
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PORITZ, JONATHAN A. "PARABOLIC VECTOR BUNDLES AND HERMITIAN-YANG-MILLS CONNECTIONS OVER A RIEMANN SURFACE." International Journal of Mathematics 04, no. 03 (June 1993): 467–501. http://dx.doi.org/10.1142/s0129167x9300025x.

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We study a certain moduli space of irreducible Hermitian-Yang-Mills connections on a unitary vector bundle over a punctured Riemann surface. The connections used have non-trivial holonomy around the punctures lying in fixed conjugacy classes of U (n) and differ from each other by elements of a weighted Sobolev space; these connections give rise to parabolic bundles in the sense of Mehta and Seshadri. We show in fact that the moduli space of stable parabolic bundles can be identified with our moduli space of HYM connections, by proving that every stable bundle admits a unique unitary gauge orbit of Hermitian-Yang-Mills connections.
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CASTRAVET, ANA-MARIA. "RATIONAL FAMILIES OF VECTOR BUNDLES ON CURVES." International Journal of Mathematics 15, no. 01 (February 2004): 13–45. http://dx.doi.org/10.1142/s0129167x0400220x.

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Let C be a smooth projective complex curve of genus g≥2 and let M be the moduli space of rank 2, stable vector bundles on C, with fixed determinant of degree 1. For any k≥1, we find all the irreducible components of the space of rational curves on M, of degree k. In particular, we find the maximal rationally connected fibrations of these components. We prove that there is a one-to-one correspondence between moduli spaces of rational curves on M and moduli spaces of rank 2 vector bundles on ℙ1×C.
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GAVIOLI, FRANCESCA. "THETA FUNCTIONS ON THE MODULI SPACE OF PARABOLIC BUNDLES." International Journal of Mathematics 15, no. 03 (May 2004): 259–87. http://dx.doi.org/10.1142/s0129167x04002272.

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In this paper we extend the result on base point freeness of the powers of the determinant bundle on the moduli space of vector bundles on a curve. We describe the parabolic analogues of parabolic theta functions, then we determine a uniform bound depending only on the rank of the parabolic bundles. In order to get this bound, we construct a parabolic analogue of Grothendieck's scheme of quotients, which parametrizes quotient bundles of a parabolic bundle, of fixed parabolic Hilbert polynomial. We prove an estimate for its dimension, which extends the result of Popa and Roth on the dimension of the Quot scheme. As an application of the theorem on base point freeness, we characterize parabolic semistability on the algebraic stack of quasi-parabolic bundles as the base locus of the linear system of the parabolic determinant bundle.
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Bhosle, Usha N., and Sanjay Kumar Singh. "Fourier–Mukai Transform on a Compactified Jacobian." International Mathematics Research Notices 2020, no. 13 (June 19, 2018): 3991–4015. http://dx.doi.org/10.1093/imrn/rny136.

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Abstract We use Fourier–Mukai transform to compute the cohomology of the Picard bundles on the compactified Jacobian of an integral nodal curve $Y$. We prove that the transform gives an injective morphism from the moduli space of vector bundles of rank $r \ge 2$ and degree $d$ ($d$ sufficiently large) on $Y$ to the moduli space of vector bundles of a fixed rank and fixed Chern classes on the compactified Jacobian of $Y$. We show that this morphism induces a morphism from the moduli space of vector bundles of rank $r \ge 2$ and a fixed determinant of degree $d$ on $Y$ to the moduli space of vector bundles of a fixed rank with a fixed determinant and fixed Chern classes on the compactified Jacobian of $Y$.
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Dey, Arijit, Sampa Dey, and Anirban Mukhopadhyay. "Statistics of moduli space of vector bundles." Bulletin des Sciences Mathématiques 151 (March 2019): 13–33. http://dx.doi.org/10.1016/j.bulsci.2018.12.003.

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BISWAS, INDRANIL, and TOMÁS L. GÓMEZ. "HECKE CORRESPONDENCE FOR SYMPLECTIC BUNDLES WITH APPLICATION TO THE PICARD BUNDLES." International Journal of Mathematics 17, no. 01 (January 2006): 45–63. http://dx.doi.org/10.1142/s0129167x06003357.

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We construct a Hecke correspondence for a moduli space of symplectic vector bundles over a curve. As an application we prove the following. Let X be a complex smooth projective curve of genus g(X) > 2 and L a line bundle over X. Let [Formula: see text] be the moduli space parametrizing stable pairs of the form (E,φ), where E is a vector bundle of rank 2n over X and φ : E ⊗ E → L a skew-symmetric nondegenerate bilinear form on the fibers of E. If deg (E) ≥ 4n(g(X)-1), then there is a projectivized Picard bundle on [Formula: see text], which is a projective bundle whose fiber over any point [Formula: see text] is ℙ(H0(X,E)). We prove that this projective bundle is stable.
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Dissertations / Theses on the topic "Moduli space of 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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Moraru, Ruxandra. "Moduli spaces of vector bundles on a Hopf surface, and their stability properties." Thesis, McGill University, 2000. http://digitool.Library.McGill.CA:80/R/?func=dbin-jump-full&object_id=37786.

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We study the moduli spaces Mn of rank two stable holomorphic SL(2, C )-bundles E over Hopf surfaces H , with c2(E) = n, and their stabilisation properties. We show that one cannot construct stabilisation maps Mn→Mn+1 that are a natural holomorphic counterpart to Taubes's subtraction procedure that is used to construct such maps in the topological case of moduli spaces of connections. We also study the fiber of a map that associates to any holomorphic bundle a graph, and show that, in certain cases, the fiber is the Jacobian of a Riemann surface. We then show that this map is a Lagrangian fibration, with respect to a Poisson structure that we will define on Mn . Finally, we generalize the notion of graph to connections, and show that the graph map thus obtained is not topologically trivial.
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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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Dyer, Ben. "NC-algebroid thickenings of moduli spaces and bimodule extensions of vector bundles over NC-smooth schemes." Thesis, University of Oregon, 2018. http://hdl.handle.net/1794/23168.

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We begin by reviewing the theory of NC-schemes and NC-smoothness, as introduced by Kapranov in \cite{Kapranov} and developed further by Polishchuk and Tu in \cite{PT}. For a smooth algebraic variety $X$ with a torsion-free connection $\nabla$, we study modules over the NC-smooth thickening $\tw \O_X$ of $X$ constructed in \cite{PT} via NC-connections. In particular we show that the NC-vector bundle $\tw E_{\bar\nabla}$ constructed via mNC-connections in \cite{PT} from a vector bundle $(E,\bar\nabla)$ with connection additionally admits a bimodule extension at least to nilpotency degree 3. Next, in joint work with A. Polishchuk \cite{DP}, we show that the gap, as first noticed in \cite{PT}, in the proof from \cite{Kapranov} that certain functors are representable by NC-smooth thickenings of moduli spaces of vector bundles is unfixable. Although the functors do not represent NC-smooth thickenings, they lead to a weaker structure of \textit{NC-algebroid thickening}, which we define. We also consider a similar construction for families of quiver representations, in particular upgrading some of the quasi-NC-structures of \cite{Toda1} to NC-smooth algebroid thickenings. This thesis includes unpublished co-authored material.
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Kaur, Inder [Verfasser]. "The C₁ conjecture for the moduli space of stable vector bundles with fixed determinant on a smooth projective curve / Inder Kaur." Berlin : Freie Universität Berlin, 2017. http://d-nb.info/1131629337/34.

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Sanna, Giangiacomo. "Rational curves and instantons on the Fano threefold Y_5." Doctoral thesis, SISSA, 2014. http://hdl.handle.net/20.500.11767/3867.

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This thesis is an investigation of the moduli spaces of instanton bundles on the Fano threefold Y_5 (a linear section of Gr(2,5)). It contains new proofs of classical facts about lines, conics and cubics on Y_5, and about linear sections of Y_5. The main original results are a Grauert-Mülich theorem for the splitting type of instantons on conics, a bound to the splitting type of instantons on lines and an SL_2-equivariant description of the moduli space in charge 2 and 3. Using these results we prove the existence of a unique SL_2-equivariant instanton of minimal charge and we show that for all instantons of charge 2 the divisor of jumping lines is smooth. In charge 3, we provide examples of instantons with reducible divisor of jumping lines. Finally, we construct a natural compactification for the moduli space of instantons of charge 3, together with a small resolution of singularities for it.
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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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Zelaci, Hacen. "Espaces de modules de fibrés vectoriels anti-invariants sur les courbes et blocs conformes." Thesis, Université Côte d'Azur (ComUE), 2017. http://www.theses.fr/2017AZUR4063/document.

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Soit X une courbe projective lisse et irréductible munie d'une involution σ. Dans cette thèse, nous étudions les fibrés vectoriels invariants and anti-invariants sur X sous l'action induite par σ. On introduit la notion de modules σ-quadratiques et on l'utilise, avec GIT, pour construire ces espaces de modules, puis on en étudie certaines propriétés. Ces espaces de modules correspondent aux espaces de modules de G-torseurs parahoriques sur la courbe X/σ , pour certains schémas en groupes parahoriques G de type Bruhat-Tits, qui sont twistés dans le cas des anti-invariants. Nous développons les systèmes de Hitchin sur ces espaces de modules et on les utilise pour dériver une classification de leurs composantes connexes en les dominant par des variétés de Prym. On étudie aussi le fibré déterminant sur les espaces de modules des fibrés vectoriels anti-invariants. Dans certains cas, ce fibré en droites admet certaines racines carrées appelées fibrés Pfaffiens. On montre que les espaces des sections globales des puissances de ces fibrés en droites (les espaces des fonctions thêta généralisées) peuvent être canoniquement identifier avec les blocs conformes associés aux algèbres de Kac-Moody affines twistées de type A(2)
Let X be a smooth irreducible projective curve with an involution σ. In this dissertation, we studythe moduli spaces of invariant and anti-invariant vector bundles over X under the induced action of σ. We introduce the notion of σ-quadratic modules and use it, with GIT, to construct these moduli spaces, and than we study some of their main properties. It turn out that these moduli spaces correspond to moduli spaces of parahoric G-torsors on the quotient curve X/σ, for some parahoric Bruhat-Tits group schemes G, which are twisted in the anti-invariant case.We study the Hitchin system over these moduli spaces and use it to derive a classification of theirconnected components using dominant maps from Prym varieties. We also study the determinant of cohomology line bundle on the moduli spaces of anti-invariant vector bundles. In some cases this line bundle admits some square roots called Pfaffian of cohomology line bundles. We prove that the spaces of global sections of the powers of these line bundles (spaces of generalized theta functions) can be canonically identified with the conformal blocks for some twisted affine Kac-Moody Lie algebras of type A(2)
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Koeppe, Thomas. "Moduli of bundles on local surfaces and threefolds." Thesis, University of Edinburgh, 2010. http://hdl.handle.net/1842/33315.

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In this thesis we study the moduli of holomorphic vector bundles over a non-compact complex space X, which will mainly be of dimension 2 or 3 and which contains a distinguished rational curve ℓ ⊂ X. We will consider the situation in which X is the total space of a holomorphic vector bundle on CP1 and ℓ is the zero section. While the treatment of the problem in this full generality requires the study of complex analytic spaces, it soon turns out that a large part of it reduces to algebraic geometry. In particular, we prove that in certain cases holomorphic vector bundles on X are algebraic. A key ingredient in the description of themoduli are numerical invariants that we associate to each holomorphic vector bundle. Moreover, these invariants provide a local version of the second Chern class. We obtain sharp bounds and existence results for these numbers. Furthermore, we find a new stability condition which is expressed in terms of these numbers and show that the space of stable bundles forms a smooth, quasi-projective variety.
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Books on the topic "Moduli space of vector bundles"

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Brambila-Paz, Leticia, Steven B. Bradlow, Oscar Garcia-Prada, and S. Ramanan, eds. Moduli Spaces and Vector Bundles. Cambridge: Cambridge University Press, 2009. http://dx.doi.org/10.1017/cbo9781139107037.

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

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Alexeev, Valery, Angela Gibney, Elham Izadi, János Kollár, Eduard Looijenga, Valery Alexeev, Angela Gibney, Elham Izadi, János Kollár, and Eduard Looijenga, eds. Compact Moduli Spaces and Vector Bundles. Providence, Rhode Island: American Mathematical Society, 2012. http://dx.doi.org/10.1090/conm/564.

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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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1944-, Maruyama Masaki, and International Taniguchi Symposium (35th : 1994 : Sanda-shi, Japan), eds. Moduli of vector bundles. New York: M. Dekker, 1996.

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

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School and Workshop on Vector Bundles and Low Codimensional Varieties (2006 Trento, Italy). Vector bundles and low codimensional subvarieties: State of the art and recent developments. [Roma]: Aracne, 2007.

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Potier, Joseph Le. Systèmes cohérents et structures de niveau. Paris: Société Mathématique de France, 1993.

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Book chapters on the topic "Moduli space of vector bundles"

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Zamora Saiz, Alfonso, and Ronald A. Zúñiga-Rojas. "Moduli Space of Vector Bundles." In SpringerBriefs in Mathematics, 59–80. Cham: Springer International Publishing, 2021. http://dx.doi.org/10.1007/978-3-030-67829-6_4.

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Balaji, V., and C. S. Seshadri. "Cohomology of a Moduli Space of Vector Bundles." In The Grothendieck Festschrift, 87–120. Boston, MA: Birkhäuser Boston, 2007. http://dx.doi.org/10.1007/978-0-8176-4574-8_4.

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Zagier, Don. "On the Cohomology of Moduli Spaces of Rank Two Vector Bundles Over Curves." In The Moduli Space of Curves, 533–63. Boston, MA: Birkhäuser Boston, 1995. http://dx.doi.org/10.1007/978-1-4612-4264-2_20.

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Kumar, Shrawan. "Infinite grassmannians and moduli spaces of G-bundles." In Vector Bundles on Curves — New Directions, 1–49. Berlin, Heidelberg: Springer Berlin Heidelberg, 1997. http://dx.doi.org/10.1007/bfb0094424.

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Hein, Georg. "Faltings’ Construction of the Moduli Space of Vector Bundles on a Smooth Projective Curve." In Affine Flag Manifolds and Principal Bundles, 91–122. Basel: Springer Basel, 2010. http://dx.doi.org/10.1007/978-3-0346-0288-4_3.

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Hacking, Paul. "Compact Moduli Spaces of Surfaces and Exceptional Vector Bundles." In Advanced Courses in Mathematics - CRM Barcelona, 41–67. Basel: Springer Basel, 2016. http://dx.doi.org/10.1007/978-3-0348-0921-4_2.

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Narasimhan, M. S. "Derived Categories of Moduli Spaces of Vector Bundles on Curves II." In Springer Proceedings in Mathematics & Statistics, 375–82. Cham: Springer International Publishing, 2018. http://dx.doi.org/10.1007/978-3-319-97379-1_16.

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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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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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Conference papers on the topic "Moduli space of vector bundles"

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Hwang, Jun-Muk. "Hecke curves on the moduli space of vector bundles over an algebraic curve." In Proceedings of the Symposium. WORLD SCIENTIFIC, 2003. http://dx.doi.org/10.1142/9789812705105_0005.

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Dominguez-Ontiveros, Elvis, Carlos Estrada-Perez, and Yassin Hassan. "Non-Intrusive Experimental Investigation of Flow Behavior Inside a 5X5 Rod Bundle With Spacer Grids Using PIV and MIR." In 17th International Conference on Nuclear Engineering. ASMEDC, 2009. http://dx.doi.org/10.1115/icone17-75214.

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The validity of the simulation results from Computational Fluid Dynamics (CFD) are still under scrutiny. Some existing CFD closure models for complex flow produce results that are generally recognized as being inaccurate. Development of improved models for complex flow simulation require an improved understanding of the detailed flow structure evolution along with dynamic interaction of the flow multi-scales. Thus, the goal of this work is to contribute to a better understanding of presupposed and existent events that could affect the safety of nuclear power plants by using state-of-the-art measurement techniques that may elucidate the fundamental physics of fluid flow in rod bundles with spacer grids. In particular, this work aims to develop an experimental data base with high spatial and temporal resolution of flow measurements inside a 5×5 rod bundles with spacer grids. The full-field detailed data base is intended to validate CFD codes at various temporal-spatial scales. Measurements were carried out using Dynamic Particle Image Velocimetry (DPIV) technique inside an optically transparent rod bundle utilizing the Matching Index of Refraction (MIR) approach. This work presents results showing full field velocity vectors and turbulence statistics for the bundle under single phase flow conditions.
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TANIGUCHI, TADASHI. "CURVATURE OF THE DETERMINANT LINE BUNDLE ON THE MODULI SPACE OF NULL-CORRELATION BUNDLES." In Proceedings in Honor of Professor K Sekigawa's 60th Birthday. WORLD SCIENTIFIC, 2005. http://dx.doi.org/10.1142/9789812701701_0019.

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ADACHI, T. "MODULI SPACE OF KILLING HELICES OF LOW ORDERS ON A COMPLEX SPACE FORM." In Proceedings of the 8th International Workshop on Complex Structures and Vector Fields. WORLD SCIENTIFIC, 2007. http://dx.doi.org/10.1142/9789812709806_0001.

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HASHIMOTO, YOSHITAKE, and KIYOSHI OHBA. "EMBEDDING OF THE MODULI SPACE OF RIEMANN SURFACES WITH IGETA STRUCTURES INTO THE SATO GRASSMANN MANIFOLD." In Proceedings of the 5th International Workshop on Complex Structures and Vector Fields. WORLD SCIENTIFIC, 2001. http://dx.doi.org/10.1142/9789812810144_0006.

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Kucherov, N., V. Kuchukov, E. Golimblevskaia, N. Kuchukova, I. Vashchenko, and E. Kuchukova. "Efficient implementation of error correction codes in modular code." In 3rd International Workshop on Information, Computation, and Control Systems for Distributed Environments 2021. Crossref, 2021. http://dx.doi.org/10.47350/iccs-de.2021.09.

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The article develops an efficient implementation of an algorithm for detecting and correcting multivalued residual errors with a fixed number of calculations of the syndrome, regardless of the set of moduli size. Criteria for uniqueness are given that can be met by selecting moduli from a set of primes to satisfy the desired error correction capability. An extended version of the algorithm with an increase in the number of syndromes depending on the number of information moduli is proposed. It is proposed to remove the restriction imposed on the size of redundant moduli. Identifying the location of the error and finding the error vector requires only look-up tables and does not require arithmetic operations. In order to minimize the excess space, an extended algorithm is also proposed in which the number of syndromes and look-up tables increases with the number of information moduli, but the locations of errors can still be identified without requiring iterative computations. By using the approximate method, we have reduced the computational complexity of the algorithm for calculating the syndrome from quadratic to linear-logarithmic, depending on the number of bits in the dynamic range.
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Benito, Ines, and Njuki W. Mureithi. "Identification of Two-Phase Flow Patterns Using Support Vector Classification." In ASME 2017 Pressure Vessels and Piping Conference. American Society of Mechanical Engineers, 2017. http://dx.doi.org/10.1115/pvp2017-65179.

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Two-phase flows are preponderant in industrial components. The present work deals with external two-phase flows across tube banks commonly found in heat exchangers, boilers and steam generators. The flows are generally highly complex and remain theoretically intractable in most cases. The two-phase flow patterns provide a convenient albeit qualitative means for describing and classifying two phase flows. The flow patterns are also closely correlated to fluid-structure interaction dynamics and thus provide a practically useful basis for the study of two-phase flow-induced vibrations. For internal two-phase flows, maps by Taitel et al. (1980) and others have led to detailed and well defined maps. For transverse flows in tube bundles, there is significantly less agreement on the flow patterns and governing parameters. The complexity of flow in tube arrays is an obvious challenge. A second difficulty is the definition of distinct flow patterns and the identification of parameters uniquely identifying the flow patterns. The present work addresses the problem of two-phase flow pattern identification in tube arrays. Flow measurements using optical as well as flow visualization via high-speed videos and photography have been conducted. To identify the flow patterns, an artificial intelligence machine learning approach was taken. Pattern classification was achieved by designing a support vector machine (SVM) classifier. The SVM achieves quantitative and non-subjective classification by mapping the flow patterns in a high dimensional mathematical space in which the different flow patterns have unique characteristics. Details of the flow measurement, parameter definition and SVM design are presented in the paper. Flow patterns identified using the SVM are presented and compared with previously identified flow patterns.
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