Calculating cohomology groups of $overline M_0,n(mathbb P^r,d)$

Abstract

Here we investigate the rational cohomology of the moduli space ℳ̄0,n (ℙr,d) of degree d stable maps from n-pointed rational curves to ℙr. We obtain partial results for small values of d with an inductive method inspired by a paper of Enrico Arbarello and Maurizio Cornalba.