1. Department of Mathematics and Physics, Mälardalen University, Västerås, Sweden;2. Georg-August-Universität Göttingen, Fakultät für Mathematik und Informatik, Göttingen, Germany
Abstract:
We compute the rational Betti cohomology groups of the coarse moduli spaces of geometrically marked Del Pezzo surfaces of degree 3 and 4 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.