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

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.