Cohomology of moduli spaces of del Pezzo surfaces. (English) Zbl 1535.14084
Summary: 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.
{© 2022 The Authors. Mathematische Nachrichten published by Wiley-VCH GmbH.}
{© 2022 The Authors. Mathematische Nachrichten published by Wiley-VCH GmbH.}
MSC:
| 14J10 | Families, moduli, classification: algebraic theory |
| 14J26 | Rational and ruled surfaces |
| 05E18 | Group actions on combinatorial structures |
| 14F40 | de Rham cohomology and algebraic geometry |
| 14F20 | Étale and other Grothendieck topologies and (co)homologies |
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