ACM line bundles on polarized K3 surfaces

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 ${\mathcal{O}}_X(D)$ on $X$ with $|D|=\varnothing$ and $D^2\ge L^2-6$ 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 $X$.

17 pages. arXiv admin note: substantial text overlap with arXiv:1407.1703