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