Rank two aCM bundles on general determinantal quartic surfaces in $\mathbb{P}^3$

TL;DR

This paper classifies rank two aCM bundles on general determinantal quartic surfaces in projective three-space, providing a comprehensive understanding of their structure and cohomological properties.

Contribution

It offers a complete classification of rank two arithmetically Cohen-Macaulay bundles on general determinantal quartic surfaces, a problem previously not fully resolved.

Findings

Classification of rank two aCM bundles on the surfaces

Identification of cohomological vanishing conditions

Structural insights into the bundles' properties

Abstract

Let $F\subseteq\mathbb{P}^3$ be a smooth determinantal quartic surface which is general in the N\"other-Lefschetz sense. In the present paper we give a complete classification of locally free sheaves $\mathcal{E}$ of rank $2$ on $F$ such that $h^1\big(F,\mathcal{E}(th)\big)=0$ for $t\in\mathbb{Z}$.