Semistability of Lazarsfeld-Mukai bundles via parabolic structures

TL;DR

This paper introduces a method to construct new semistable Lazarsfeld-Mukai bundles on smooth projective surfaces using parabolic structures, and explores their stability and orbifold bundle relations.

Contribution

It develops a framework linking parabolic vector bundles to Lazarsfeld-Mukai bundles, producing new examples of semistable bundles on surfaces and their covers.

Findings

Constructed semistable Lazarsfeld-Mukai bundles via parabolic structures.

Established orbifold bundle correspondence on Kawamata covers.

Produced new semistable bundles on projective plane and K3 surfaces.

Abstract

Our aim in this article is to produce new examples of semistable Lazarsfeld- Mukai bundles on smooth projective surfaces $X$ using the notion of parabolic vector bundles. In particular, we associate natural parabolic structures to any rank two (dual) Lazarsfeld-Mukai bundle and study the parabolic stability of these parabolic bundles. We also show that the orbifold bundles on Kawamata coverings of $X$ corresponding to the above parabolic bundles are themselves certain (dual) Lazarsfeld-Mukai bundles. This gives semistable Lazarsfeld-Mukai bundles on Kawamata covers of the projective plane and of certain K3 surfaces.