The Frobenius morphism on a toric variety

Abstract

We give a characteristic p proof of the Bott vanishing theorem for projective toric varieties using that the Frobenius morphism on a toric variety lifts to characteristic p 2 .A proof of the Bott vanishing theorem was previously known only in the simplicial case.We also generalize the work of Paranjape and Srinivas about non-liftability to characteristic zero of the Frobenius morphism on flag varieties by showing that Bott vanishing fails for a large class of flag varieties not isomorphic to a product of projective spaces.

Locations

• Tohoku Mathematical Journal - View - PDF