Equivariant Cohomology of Certain Moduli of Weighted Pointed Rational Curves

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.