The cohomology of real De Concini-Procesi models of Coxeter type. (English) Zbl 1153.14011

Henderson, Anthony; Rains, Eric

Int. Math. Res. Not. 2008, Article ID rnn001, 29 p. (2008).

The aim of the paper is to study the rational cohomology groups of the real De Concini-Procesi model corresponding to a finite Coxeter group. This is a generalization of the type A case of the moduli space of stable genus zero curves with marked points. The formulae for the Betti numbers in types B and D are given, and exact values of the Betti numbers in exceptional types are computed. The authors also find a generating function for the characters of the representations of a Coxeter group of type B on the rational cohomology groups of the corresponding De Concini-Procesi model, and deduce the multiplicities of one-dimensional characters in the representations, and a formula for the Euler character. A moduli space interpretation of this type B variety is obtained: it is embedded as a closed subvariety in \(\overline{\mathcal{M}_{0,2n+2}}\).

Reviewer: Ivan V. Arzhantsev (Moskva)

MSC:

14D20	Algebraic moduli problems, moduli of vector bundles
14N20	Configurations and arrangements of linear subspaces
20F55	Reflection and Coxeter groups (group-theoretic aspects)

Keywords:

the De Concini-Procesi model; cohomology; Coxeter groups; moduli spaces