Rank two aCM bundles on the del Pezzo fourfold of degree $6$ and its general hyperplane section

Abstract

In the present paper we completely classify locally free sheaves of rank $2$ with vanishing intermediate cohomology modules on the image of the Segre embedding ${\mathbb{P}}^2\times {\mathbb{P}}^2\subseteq {\mathbb{P}}^8$ and its general hyperplane sections. Such a classification extends similar already known results regarding del Pezzo varieties with Picard numbers $1$ and $3$ and dimension at least $3$.

23 pages, 1 figure. arXiv admin note: text overlap with arXiv:1306.6008