Some remarks on rigid sheaves, helices and exceptional vector bundles on Fano varieties over arbitrary fields

Abstract

In this paper we study the connection between rigid sheaves and separable-exceptional objects on Fano varieties over arbitrary fields. We give criteria for a rigid vector bundle on a Fano variety to be the direct sum of separable-exceptional bundles and for a separable-exceptional vector bundle to be part of a full separable-exceptional collection.

revised version, 13 pages, comments are welcome

References in corpus (3)

• Semiorthogonal decompositions in algebraic geometry
• Non-existence of exceptional collections on twisted flags and categorical representability via noncommutative motives
• Absolutely split locally free sheaves on proper $k$-schemes and Brauer--Severi varieties