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Cohomology of moduli spaces of Del Pezzo surfaces
Authors:Olof Bergvall  Frank Gounelas
Institution: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.
Keywords:cohomology of moduli  cubic surface  Del Pezzo surface  hyperplane arrangements
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