On minimal models of projective Hyperkaehler manifolds

TL;DR

This paper proves that minimal models of projective Hyperkaehler manifolds are themselves Hyperkaehler, impacting the understanding of moduli spaces of sheaves on K3 surfaces and their birational properties.

Contribution

It establishes that minimal models of projective Hyperkaehler manifolds are Hyperkaehler, clarifying their structure and birational relationships with moduli spaces.

Findings

Minimal models of projective Hyperkaehler manifolds are Hyperkaehler.

Moduli spaces of sheaves on K3 surfaces without symplectic resolutions are not birational to Hyperkaehler manifolds.

Abstract

Any minimal model of a projective Hyperkaehler manifold is a projective Hyperkaehler manifold. As a consequence, moduli spaces of sheaves on a k3 that don't admit a symplectic resolution are not birational to Hyperkaehler manifolds.