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

Let $F\subseteq\mathbb{P}^3$ be a smooth determinantal quartic surface which is general in the Nöther-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 $t\in\mathbb{Z}$.

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