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

TL;DR

This paper characterizes initialized and ACM line bundles of rank 1 on a smooth sextic surface in projective 3-space, providing insights into their structure relative to hyperplane sections.

Contribution

It offers a new characterization of rank 1 ACM bundles on a sextic surface, advancing understanding of their geometric properties.

Findings

Classification of rank 1 ACM bundles on the sextic surface

Conditions for bundles to be initialized and ACM

Relationship between bundles and hyperplane sections

Abstract

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 $X$.