%0 Journal Article %T Calculating cohomology groups of moduli spaces of curves via algebraic geometry %A Enrico Arbarello %A Maurizio Cornalba %J Mathematics %D 1998 %I arXiv %X We compute the first, second, third, and fifth rational cohomology groups of the moduli space of stable n-pointed genus g curves, for all g and n, using (mostly) algebro-geometric techniques. %U http://arxiv.org/abs/math/9803001v1