Equivariant Cohomology of Certain Moduli of Weighted Pointed Rational Curves

TL;DR

This paper computes the symmetric group actions on the cohomology of specific moduli spaces of weighted pointed rational curves, providing formulas for equivariant Poincaré polynomials for small cases.

Contribution

It determines the symmetric group action on cohomology of moduli spaces of weighted pointed rational curves and offers a method to compute equivariant Poincaré polynomials.

Findings

Explicit formulas for equivariant Poincaré polynomials for small m and n.

Description of the symmetric group action on the cohomology.

Method for calculating the equivariant cohomology of these moduli spaces.

Abstract

We determine the action of the product of symmetric groups on the cohomology of certain moduli of weighted pointed rational curves. The moduli spaces that we study are of stable rational curves with m+n marked points where the first m marked points are distinct from all the others where as the last n may coincide among themselves. We give a recipe for calculating the equivariant Poincar\'e polynomials and list them for small m and n.