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Zbl 1153.14011
Henderson, Anthony; Rains, Eric
The cohomology of real De Concini-Procesi models of Coxeter type. (English)
[J] Int. Math. Res. Not. 2008, Article ID rnn001, 29 p. (2008). ISSN 1073-7928; ISSN 1687-0247/e

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 $\overline{\Cal{M}_{0,2n+2}}$.
[Ivan V. Arzhantsev (Moskva)]

MSC 2000:: *14D20 Algebraic moduli problems
14N20 Configurations of linear subspaces
20F55 Coxeter groups

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

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Zentralblatt MATH Berlin [Germany]