On the Shafarevich conjecture for irreducible symplectic varieties

TL;DR

This paper proves the Shafarevich conjecture for irreducible symplectic varieties within a fixed deformation class, extending known results for K3 surfaces to higher dimensions, and discusses related cohomological generalizations.

Contribution

It establishes the Shafarevich conjecture for a class of higher-dimensional symplectic varieties, a significant extension of previous results for K3 surfaces.

Findings

Shafarevich conjecture holds for fixed deformation class

Second cohomological generalization does not hold in general

Proposes alternative cohomological formulations

Abstract

Irreducible symplectic varieties are higher-dimensional analogues of K3 surfaces. In this paper, we prove the Shafarevich conjecture for irreducible symplectic varieties of fixed deformation class. We also observe that the second cohomological generalization of the Shafarevich conjecture does not hold in general, and discuss another formulation of a cohomological generalization.