On the localization theorem in equivariant cohomology

TL;DR

This paper provides a straightforward proof of the localization theorem in equivariant cohomology and applies it to describe the cohomology algebra of certain symplectic varieties with group actions.

Contribution

It offers a simplified proof of the localization theorem and extends its application to compact symplectic varieties with multiplicity-free group actions.

Findings

Simplified proof of the localization theorem in equivariant cohomology

Description of cohomology algebra for compact symplectic varieties

Application to smooth, projective spherical varieties

Abstract

We present a simple proof of a precise version of the localization theorem in equivariant cohomology. As an application, we describe the cohomology algebra of any compact symplectic variety with a multiplicity-free action of a compact Lie group. This applies in particular to smooth, projective spherical varieties.