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

TL;DR

This paper characterizes aCM line bundles on smooth quintic hypersurfaces in projective 3-space, providing necessary and sufficient conditions for their initialization and aCM property relative to hyperplane sections.

Contribution

It offers a complete characterization of aCM line bundles on quintic hypersurfaces, detailing conditions for their initialization and aCM status.

Findings

Provides necessary and sufficient conditions for aCM line bundles

Characterizes line bundles with respect to hyperplane sections

Enhances understanding of vector bundles on quintic hypersurfaces

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 $H$.