Locally trivial monodromy of moduli spaces of sheaves on Abelian surfaces

TL;DR

This paper describes the locally trivial monodromy group of certain singular moduli spaces of sheaves on Abelian surfaces, extending previous results to non-primitive cases and proving the SYZ conjecture for these spaces.

Contribution

It extends the description of the monodromy group to non-primitive Mukai vectors and proves the SYZ conjecture for singular moduli spaces of sheaves on Abelian surfaces.

Findings

Locally trivial monodromy group is isomorphic to that of smooth moduli spaces.

Extension of Markman's and Mongardi's results to non-primitive cases.

Proof of the SYZ conjecture for these singular moduli spaces.

Abstract

The aim of this work is to give a description of the locally trivial monodromy group of irreducible symplectic varieties arising from moduli spaces of semistable sheaves on Abelian surfaces with non-primitive Mukai vector. The outcome is that the locally trivial monodromy group of a singular moduli space of this type is isomorphic to the monodromy group of a smooth moduli space, extending Markman's and Mongardi's description to the non-primitive case. As a consequence, we also prove the SYZ conjecture for any singular moduli space of this type.