ACM line bundles on polarized K3 surfaces

2018/03/30 by Watanabe, Kenta
#14H60 #14J28 #Algebraic Geometry (math.AG) #Computational Geometry (cs.CG) #FOS: Computer and information sciences #FOS: Mathematics

paper · doi:10.48550/arxiv.1804.00719

Abstract

An ACM bundle on a polarized algebraic variety is defined as a vector bundle whose intermediate cohomology vanishes. We are interested in ACM bundles of rank one with respect to a very ample line bundle on a K3 surface. In this paper, we give a necessary and sufficient condition for a non-trivial line bundle O_X(D) on X with |D|=∅ and D²≥ L²-6 to be an ACM and initialized line bundle with respect to L, for a given K3 surface X and a very ample line bundle L on X.

Related

• ACM bundles on K3 surfaces of genus 2
• aCM vector bundles on projective surfaces of nonnegative Kodaira\n dimension
• On initialized and ACM line bundles over a smooth sextic surface in \mathbb P³
• On polarized surfaces of low degree whose adjont bundles are not spanned
• Existence of ACM Bundles on Polarized Abelian Varieties