ACM bundles of rank 2 on quartic hypersurfaces in ℙ³ and Lazarsfeld-Mukai bundles

2020/01/01 by K. Watanabe, Watanabe, Kenta
Mathematics · #14J28 #14J60 #14J70 #Advanced Algebra and Geometry #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Geometric Analysis and Curvature Flows

paper · pdf · doi:10.48550/arxiv.2001.00199

openalex publication_date 2020/01/01 · openalex created_date 2022/10/02 · openalex updated_date 2026/07/28

Abstract

Let X be a smooth quartic hypersurface in ℙ³. By the Brill-Noether theory of curves on K3 surfaces, if a rank 2 aCM bundle on X is globally generated, then it is the Lazarsfeld-Mukai bundle E_C,Z associated with a smooth curve C on X and a base point free pencil Z on C. In this paper, we will focus on the classification of such bundles on X to investigate aCM bundles of rank 2 on X. Concretely, we will give a necessary condition for a rank 2 vector bundle of type E_C,Z to be indecomposable initialized and aCM, in the case where the class of C in Pic(X) is contained in the sublattice of rank 2 generated by the hyperplane class of X and a non-trivial initialized aCM line bundle on X.

Related

• The classification of ACM line bundles on quartic hypersurfaces on P³
• Examples of rank two aCM bundles on smooth quartic surfaces in ℙ³
• Rank two aCM bundles on general determinantal quartic surfaces in ℙ³
• Slope semistability of rank 2 Lazarsfeld-Mukai bundles on K3 surfaces and ACM line bundles
• ACM bundles on K3 surfaces of genus 2