On initialized and ACM line bundles over a smooth sextic surface in ${\mathbb{P}}^3$

Let $X\subset {\mathbb{P}}^3$ be a smooth hypersurface of degree $6$ over complex numbers. In this paper, we give a characterization of initialized and ACM bundles of rank $1$ on $X$ with respect to the line bundle given by a smooth hyperplane section of $X$.