The characterization of aCM line bundles on quintic hypersurfaces in $\mathbb{P}^3$

Abstract

Let $X$ be a smooth quintic hypersurface in $\mathbb{P}^3$, let $C$ be a smooth hyperplane section of $X$, and let $H=\mathcal{O}_X(C)$. In this paper, we give a necessary and sufficient condition for the line bundle given by a non-zero effective divisor on $X$ to be initialized and aCM with respect to $H$.