Lazarsfeld-Mukai bundles on K3 surfaces associated to a pencil computing Clifford index

TL;DR

This paper investigates the semistability of Lazarsfeld-Mukai bundles on K3 surfaces associated with pencils that compute the Clifford index of curves, providing a complete criterion for their semistability.

Contribution

It establishes a necessary and sufficient condition for the semistability of Lazarsfeld-Mukai bundles related to Clifford index computations on K3 surfaces.

Findings

Characterization of semistability conditions for Lazarsfeld-Mukai bundles

Complete criterion for semistability based on geometric data

Insights into the relationship between Clifford index and bundle stability

Abstract

Let $X$ be a smooth projective K3 surface over complex numbers and $C$ be an ample curve on $X$. In this paper we will study the semistability of the Lazarsfeld-Mukai bundle $E_{C, A}$ associated to a line bundle $A$ ion $C$ such that $|A|$ is a pencil on $C$ and computes the Clifford index of $C$. We give a necessary and sufficient condition for $E_{C, A}$ being semistable.