Cohomology of line bundles on horospherical varieties

Abstract

A horospherical variety is a normal algebraic variety where a connected reductive algebraic group acts with an open orbit isomorphic to a torus bundle over a flag variety. In this article we study the cohomology of line bundles on complete horospherical varieties. The main tool in this article is the machinery of Grothendieck–Cousin complexes, and we also prove a Kunneth-like formula for local cohomology.