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

2015/03/23 by K. Watanabe, Watanabe, Kenta
Mathematics · #14H51 #14J28 #14J60 #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Geometry and complex manifolds #Homotopy and Cohomology in Algebraic Topology

paper · pdf · doi:10.48550/arxiv.1503.06682

openalex publication_date 2015/03/23 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28

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 O_X(C). In this paper, we will give a sufficient condition for such a Lazarsfeld-Mukai bundle E_C,Z to be O_X(C)-slope semistable by ACM line bundles with respect to O_X(C).

Related

• Unstable Lazarsfeld-Mukai bundles of rank 2 on a certain K3 surface of Picard number 2
• Semistability of Lazarsfeld-Mukai bundles via parabolic structures
• Restricted Lazarsfeld-Mukai bundles and canonical curves
• ACM bundles of rank 2 on quartic hypersurfaces in ℙ³ and Lazarsfeld-Mukai bundles
• CM-line bundles and slope \K-semistability for big and nef line bundles along subschemes