Slope semistability of rank 2 Lazarsfeld-Mukai bundles on K3 surfaces and ACM line bundles

TL;DR

This paper investigates the slope semistability of rank 2 Lazarsfeld-Mukai bundles on K3 surfaces, providing conditions involving ACM line bundles that ensure semistability.

Contribution

It offers a new sufficient condition for the slope semistability of Lazarsfeld-Mukai bundles on K3 surfaces based on ACM line bundles.

Findings

Provides a criterion for slope semistability using ACM line bundles

Focuses on rank 2 Lazarsfeld-Mukai bundles on K3 surfaces

Enhances understanding of vector bundle stability on algebraic surfaces

Abstract

Previously, many people have studied a stability of vector bundles of given rank and Chern classes on algebraic varieties. Recently, we are interested in the slope stability of the rank 2 Lazarsfeld-Mukai bundle $E_{C,Z}$ on a K3 surface $X$ associated to a very ample smooth curve $C$ on $X$ and a base point free pencil $Z$ on $C$ with respect to $\mathcal{O}_X(C)$. In this paper, we will give a sufficient condition for such a Lazarsfeld-Mukai bundle $E_{C,Z}$ to be $\mathcal{O}_X(C)$-slope semistable by ACM line bundles with respect to $\mathcal{O}_X(C)$.