ℓ-away ACM line bundles on a nonsingular cubic surface

Abstract

Let XCP3 be a nonsingular cubic hypersurface. Faenzi ([8]) and later Pons-Llopis and Tonini ([21]) have completely characterized ACM line bundles over X. As a natural continuation of their study in the non-ACM direction, in this paper, we completely classify ℓ -away ACM line bundles (introduced recently by Gawron and Genc ([9])) over X, when . For , we give examples of -away ACM line bundles on X and for each , we establish the existence of smooth hypersurfaces of degree in admitting -away ACM line bundles.