LAUSR

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 $${\mathcal {O}}_X(D)$$OX(D) on X with $$|D|\ne \emptyset $$|D|≠∅ and $$D^2\ge L^2-6$$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.