Results 11 to 20 of about 633 (249)
Parallels between Moduli of Quiver Representations and Vector Bundles over Curves [PDF]
Symmetry, Integrability and Geometry: Methods and Applications, 2018 This is a review article exploring similarities between moduli of quiver representations and moduli of vector bundles over a smooth projective curve. After describing the basic properties of these moduli problems and constructions of their moduli spaces via geometric invariant theory and symplectic reduction, we introduce their hyperkähler analogues ...
Hoskins, V.
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Ulrich bundles on a general blow–up of the plane [PDF]
, 2023 We prove that on Xn, the plane blown–up at n general points, there are Ulrich line bundles with respect to a line bundle corresponding to curves of degree m passing simply through the n blown–up points, with m less than or equal to 2 times the square ...
Ciliberto, Ciro +6 more
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A stratification of the moduli space of vector bundles on curves [PDF]
Journal für die reine und angewandte Mathematik (Crelles Journal), 1998 Let $E$ be a vector bundle of rank $r\geq 2$ on a smooth projective curve $C$ of genus $g \geq 2$ over an algebraically closed field $K$ of arbitrary characteristic. For any integer with $1\le k\le r-1$ we define $${\se}_k(E):=k°E-r\max°F.$$ where the maximum is taken over all subbundles $F$ of rank $k$ of $E$. The ${s}_k$ gives a stratification of the
Brambila-Paz, L., Lange, Herbert
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Moduli spaces of vector bundles on a curve and opers
Proceedings - Mathematical Sciences, 2023 Let $X$ be a compact connected Riemann surface of genus $g$, with $g\, \geq\,2$, and let $ξ$ be a holomorphic line bundle on $X$ with $ξ^{\otimes 2}\,=\, {\mathcal O}_X$. Fix a theta characteristic $\mathbb L$ on $X$. Let ${\mathcal M}_X(r,ξ)$ be the moduli space of stable vector bundles $E$ on $X$ of rank $r$ such that $\bigwedge^r E\,=\, ξ$ and $H^0 ...
Biswas, Indranil +2 more
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Rationality of moduli of vector bundles on curves
Indagationes Mathematicae, 1999 21 pages, Latex2e (with AMS packages)
Schofield, AH, King, A
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Geometry of the moduli of parabolic bundles on elliptic curves
, 2021 International audienceThe goal of this paper is the study of simple rank 2 parabolic vector bundles over a 2-punctured elliptic curve C. We show that the moduli space of these bundles is a non-separated gluing of two charts isomorphic to ℙ^1×ℙ^1. We also
Vargas, Néstor Fernández +1 more
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Maximality of moduli spaces of vector bundles on curves
Épijournal de Géométrie Algébrique, 2023 We prove that moduli spaces of semistable vector bundles of coprime rank and degree over a non-singular real projective curve are maximal real algebraic varieties if and only if the base curve itself is maximal. This provides a new family of maximal varieties, with members of arbitrarily large dimension.
Brugallé, E., Schaffhauser, F.
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Projectivity of the moduli space of vector bundles on a curve
, 2022 We discuss the projectivity of the moduli space of semistable vector bundles on a curve of genus $g\geq 2$. This is a classical result from the 1960s, obtained using geometric invariant theory. We outline a modern approach that combines the recent machinery of good moduli spaces with determinantal line bundle techniques.
Alper, Jarod +4 more
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Calabi–Yau threefolds and moduli of abelian surfaces I [PDF]
, 2001 We describe birational models and decide the rationality/unirationality of moduli spaces $\cal A$d (and $\cal A$levd) of (1, d)-polarized Abelian surfaces (with canonical level structure, respectively) for small values of d.
Sorin Popescu +3 more
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Geometry and derived categories of holomorphic symplectic manifolds [PDF]
, 2022 In this thesis we study various aspects of hyper-Kähler manifolds and abelian varieties such as their derived categories, sheaves, cycles, and topology. The thesis consists of six parts. The first part is mostly a survey of results of Taelman.
Beckmann, Thorsten Michael
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