Calculating cohomology groups of ℳ̄ 0, n (ℙ r , d )

Abstract

Here we investigate the rational cohomology of the moduli space ℳ̄ 0, n (ℙ r , d ) of degree d stable maps from n -pointed rational curves to ℙ r . We obtain partial results for small values of d with an inductive method inspired by a paper of Enrico Arbarello and Maurizio Cornalba.