ACM line bundles on polarized K3 surfaces

03/30/2018

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by   Kenta Watanabe, et al.

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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 D^2≥ 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.