Cohomology of line bundles on horospherical varieties

TL;DR

This paper investigates the cohomology of line bundles on complete horospherical varieties, expanding understanding of their geometric and algebraic properties.

Contribution

It provides new insights into the cohomology of line bundles specifically on complete horospherical varieties, a class of algebraic varieties with group actions.

Findings

Characterization of cohomology groups for line bundles on horospherical varieties

Conditions for vanishing and non-vanishing of cohomology

Explicit computations in specific cases

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.