On the period of Li, Pertusi and Zhao's symplectic variety

TL;DR

This paper extends classical results on moduli spaces of sheaves to Bridgeland semistable objects on cubic fourfolds, determining their periods and birational relations to K3 surface moduli spaces.

Contribution

It generalizes known results to a broader class of moduli spaces, providing new insights into their periods and birational geometry.

Findings

Determined the period of these moduli spaces.

Identified conditions for birational equivalence to K3 surface moduli.

Extended classical results to Bridgeland stability on cubic fourfolds.

Abstract

We extend classical results of Perego and Rapagnetta on moduli spaces of sheaves of type OG10 to moduli spaces of Bridgeland semistable objects on the Kuznetsov component of a cubic fourfold. In particular, we determine the period of this class of varieties and use it to understand when they become birational to moduli spaces of sheaves on a K3 surface.