Extension of 2-forms and symplectic varieties

TL;DR

This paper explores symplectic varieties lacking symplectic resolutions, including moduli spaces on K3 surfaces and symplectic V-manifolds, proving a local Torelli theorem and discussing symplectic singularities.

Contribution

It extends the theory of 2-forms to symplectic varieties without resolutions and proves a local Torelli theorem for these complex structures.

Findings

Proved local Torelli theorem for certain symplectic varieties

Analyzed properties of symplectic singularities

Studied moduli spaces of sheaves on K3 surfaces

Abstract

This paper deals with symplectic varieties which do not have symplectic resolutions. Some moduli spaces of semi-stable torsion-free sheaves on a K3 surface, and symplectic V-manifolds are such varieties. We shall prove local Torelli theorem for symplectic varieties. Some results on symplectic singularities are also included.