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

Gianfranco Casnati (1) , Daniele Faenzi (2) , Francesco Malaspina (1)

1 Dipartimento di Scienze Matematiche
2 IMB - Institut de Mathématiques de Bourgogne [Dijon]

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 $\mathbb{P}^2$ x $\mathbb{P}^2 \subseteq \mathbb{P}^8$ 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.

Domaines: Géométrie algébrique [math.AG]

Gianfranco Casnati, Daniele Faenzi, Francesco Malaspina. Rank two aCM bundles on the del Pezzo fourfold of degree 6 and its general hyperplane section. Journal of Pure and Applied Algebra, 2018, 222 (3), pp.585-609. ⟨10.1016/j.jpaa.2017.04.021⟩. ⟨hal-01660679⟩