Cohomology of moduli spaces of Del Pezzo surfaces

Abstract

We compute the rational Betti cohomology groups of the coarse moduli spaces of geometrically marked Del Pezzo surfaces of degree three and four as representations of the Weyl groups of the corresponding root systems. The proof uses a blend of methods from point counting over finite fields and techniques from arrangement complements.

arXiv commentFurther applications given in the introduction. Final version, to appear Math. Nachrichten