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

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.

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References in corpus (2)

• Slope semistability of rank 2 Lazarsfeld-Mukai bundles on K3 surfaces and ACM line bundles
• An elementary proof of Lelli Chiesa's theorem on constancy of second coordinate of gonality sequence