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

Abstract

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