On the derived category of coherent sheaves on a 5-dimensional Fano variety

Abstract

Let LG 3 C be the Grassmannian of Lagrangian planes in a six-dimensional vector space V. It is a six-dimensional Fano variety of index 4. Consider its smooth hyperplane section. We show that in the derived category of coherent sheaves on such a hyperplane section there exists an exceptional collection, generating the derived category. To cite this article: A. Samokhin, C. R. Acad. Sci. Paris, Ser. I 340 (2005).