Locally trivial monodromy of moduli spaces of sheaves on Abelian surfaces

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.