Moduli spaces of sheaves on K3 surfaces

TL;DR

This survey reviews the theory of moduli spaces of sheaves on K3 surfaces, highlighting key developments, applications, and recent advances in understanding their geometric and algebraic properties.

Contribution

It compiles and explains recent progress in the study of moduli spaces of sheaves on K3 surfaces, including applications to Chow rings and stability conditions.

Findings

Descriptions of moduli spaces of stable sheaves on K3 surfaces

Recent results on Chow rings and ample cones of related manifolds

Advances in Bridgeland stability and complex moduli spaces

Abstract

In this survey article we describe moduli spaces of simple, stable, and semistable sheaves on K3 surfaces, following the work of Mukai, O'Grady, Huybrechts, Yoshioka, and others. We also describe some recent developments, including applications to the study of Chow rings of K3 surfaces, determination of the ample and nef cones of irreducible holomorphic symplectic manifolds, and moduli spaces of Bridgeland stable complexes of sheaves.