Torus actions and tensor products of intersection cohomology

TL;DR

This paper explores how tensor products of intersection cohomology sheaves on projective varieties with torus actions relate to their individual cohomology groups, including equivariant cohomology cases.

Contribution

It establishes new relationships between cohomology groups of tensor products and individual sheaves under torus actions, extending to equivariant cohomology.

Findings

Cohomology of tensor products can be expressed in terms of individual sheaves.

Results apply to both ordinary and equivariant cohomology.

Provides new tools for studying intersection cohomology in algebraic geometry.

Abstract

Given certain intersection cohomology sheaves on a projective variety with a torus action, we relate the cohomology groups of their tensor product to the cohomology groups of the individual sheaves. We also prove a similar result in the case of equivariant cohomology.