Moduli spaces of stable sheaves on abelian surfaces

2000/09/01 by Kōta Yoshioka, Kota Yoshioka, Yoshioka, Kota · 8 citations
Computer Science · Mathematics · #14d20 #Advanced Algebra and Geometry #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Polynomial and algebraic computation #math.AG #msc:14d20

paper · pdf · doi:10.48550/arxiv.math/0009001

37 pages, references added, organization is changed

openalex publication_date 2000/09/01 · arxiv created 2001/04/25 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper, we consider moduli spaces of stable sheaves on abelian surfaces. Our main assumption is the primitivity of the associated Mukai vector. We construct many isomorphisms of muduli spaces induced by Fourier-Mukai functor. As an application, we show that deformation type of these spaces are determined by their dimension. We next show that the fiber of the albanese map is irreducible symplectic manifolds In particular, we describe the period by using Mukai lattice. We also discuss deformation type of moduli spaces of stable sheaves on K3 surfaces.

Cited by

• The Lefschetz standard conjectures for 4d-dimensional Kummer-type hyper-Kaehler varieties
• Stabilization of intersection Betti numbers for moduli spaces of one-dimensional sheaves on surfaces
• Hilbert squares of genus 16 K3 surfaces
• The SYZ conjecture for singular moduli spaces of sheaves on K3 surfaces
• From Hitchin Systems to Rational Elliptic Surfaces with C*-actions via Orbifold Hilbert Schemes
• Nef cones of Hilbert schemes of points on some K3 surfaces
• Hilbert schemes of elliptic surfaces: group actions and derived categories
• Preservation of stability under the Fourier-Mukai transform whose kernel is the Poincare line bundle

Related

• Albanese map of moduli of stable sheaves on abelian surfaces
• Some examples of isomorphisms induced by Fourier-Mukai functors
• Irreducibility of moduli spaces of vector bundles on K3 surfaces
• A Note on Singular Moduli Spaces of Sheaves on K3 Surfaces
• Irreducible symplectic varieties from moduli spaces of sheaves on K3 and Abelian surfaces