Irreducible symplectic varieties from moduli spaces of sheaves on K3 and Abelian surfaces

TL;DR

This paper proves that moduli spaces of sheaves on K3 and Abelian surfaces are irreducible symplectic varieties, expanding understanding of their geometric structure and symplectic properties.

Contribution

It establishes the irreducibility and symplectic nature of moduli spaces of sheaves on K3 and Abelian surfaces, a significant advancement in algebraic geometry.

Findings

Moduli spaces on K3 surfaces are irreducible symplectic varieties.

Fibers of the Albanese map on Abelian surfaces are irreducible symplectic.

Supports the broader classification of moduli spaces in algebraic geometry.

Abstract

We show that the moduli spaces of sheaves on a projective K3 surface are irreducible symplectic varieties, and that the same holds for the fibers of the Albanese map of moduli spaces of sheaves on an Abelian surface.