The equivariant cohomology of weighted projective space

TL;DR

This paper characterizes the integral equivariant cohomology ring of weighted projective spaces using piecewise polynomials, establishing it as a complete invariant and deriving a Chern class formula for weighted projective bundles.

Contribution

It provides a new description of the equivariant cohomology ring of weighted projective spaces and introduces a Chern class formula for weighted projective bundles.

Findings

The equivariant cohomology ring is described via generators and relations.

The ring is shown to be a perfect invariant.

A Chern class formula for weighted projective bundles is proved.

Abstract

We describe the integral equivariant cohomology ring of a weighted projective space in terms of piecewise polynomials, and thence by generators and relations. We deduce that the ring is a perfect invariant, and prove a Chern class formula for weighted projective bundles.