Connected components of moduli spaces of irreducible holomorphic symplectic manifolds of Kummer type

TL;DR

This paper investigates the connected components of moduli spaces of certain irreducible holomorphic symplectic manifolds, extending previous results from K3 surfaces to generalized Kummer varieties.

Contribution

It generalizes Apostolov's counting of connected components from Hilbert schemes of K3 surfaces to generalized Kummer varieties.

Findings

Counted the number of connected components for these moduli spaces.

Extended known results to a broader class of symplectic manifolds.

Provided new insights into the topology of moduli spaces.

Abstract

Moduli spaces of polarised (with fixed polarisation type) irreducible holomorphic symplectic manifolds deformation equivalent to Hilbert schemes of points on $K3$ surfaces are not connected in general and A. Apostolov counted the number of their components. We extend Apostolov's results to the case of manifolds deformation equivalent to generalised Kummer varieties.