Examples of rank two aCM bundles on smooth quartic surfaces in ${\mathbb{P}}^3$

Abstract

Let $F\subseteq {\mathbb{P}}^3$ be a smooth quartic surface and let ${\mathcal{O}}_F(h):={\mathcal{O}}_{{\mathbb{P}}^3}(1)\otimes {\mathcal{O}}_F$. In the present paper we classify locally free sheaves $\mathcal{E}$ of rank $2$ on $F$ such that $c_1(\mathcal{E})={\mathcal{O}}_F(2h)$, $c_2(\mathcal{E})=8$ and $h^1(F,\mathcal{E}(th))=0$ for $t\in \mathbb{Z}$. We also deal with their stability.

22 pages. Exposition improved