Tilting bundles via the Frobenius morphism

Abstract

We show how to construct tilting bundles for a class of smooth projective varieties using characteristic $p$ methods. Given such a variety $X$, reduce it modulo a prime number and consider the direct image of the structure sheaf under the Frobenius morphism. We prove that under suitable restrictions on the characteristic, these direct images are tilting bundles for some toric Fano varieties, Del Pezzo surfaces, and flag varieties $G/B$ of type $A_2$ and $B_2$.

37 pages. This is a revised and extended version of an earlier preprint available at http://www.mpim-bonn.mpg.de/Research/MPIM+Preprint+Series/

References in corpus (2)

• Noncommutative Counterparts of the Springer Resolution
• Direct images of bundles under Frobenius morphisms

Cited by in corpus (4)

• Some observations on Karoubian complete strongly exceptional posets on the projective homogeneous varieties
• Exceptional collections on toric Fano threefolds and birational geometry
• The Frobenius morphism on flag varieties, II
• On the D-affinity of flag varieties in positive characteristic