Classifying the irreducible components of moduli stacks of torsion free sheaves on K3 surfaces and an application to Brill-Noether theory

TL;DR

This paper classifies the irreducible components of moduli stacks of rank 2 torsion free sheaves on K3 surfaces and applies this to understand the structure of Brill-Noether loci on Hilbert schemes.

Contribution

It provides a classification of irreducible components for these moduli stacks on K3 surfaces, extending previous work on ruled surfaces and applying to Brill-Noether theory.

Findings

Classified irreducible components of moduli stacks on K3 surfaces.

Extended classification to Brill-Noether loci of Hilbert schemes.

Connected geometric structures with sheaf moduli and Brill-Noether theory.

Abstract

In this article, we classify the irreducible components of moduli stacks of torsion free sheaves of rank 2 on K3 surfaces of Picard number 1. For ruled surfaces, the components of moduli stacks of torsion free sheaves were classified by C.Walter. Moreover, by virtue of our result, we classify the irreducible components of Brill-Noether loci of Hilbert schemes of points on K3 surfaces.