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Zbl 1213.14102
Rains, Eric M.
The homology of real subspace arrangements. (English)
[J] J. Topol. 3, No. 4, 786-818 (2010). ISSN 1753-8416; ISSN 1753-8424/e

Let $V$ be a vector space and let $G$ be a {\it building set}, i.e. a finite collection of subspaces of the dual $V^*$, whose elements are indecomposable. The open set $V-\bigcup_{H_i\in G} H_i^\perp$ has a natural emebdding in the product of the projective spaces $\Bbb P(V/H_i^\perp)$. The closure $Y_G$ of the image is the De Concini--Procesi model of $G$. The variety $Y_G$, in the case where $G$ is a braid arrangement, is connected with the real part of the closure of the moduli space $\bar M_{0,n}(\Bbb R)$ of marked rational curves. Starting with a combinatorial description of the homology of $V-\bigcup_{H_i\in G} H_i^\perp$, it is possible to characterize the homology of $\bar M_{0,n}(\Bbb R)$. The author performs a similar analysis when $G$ is a general building set. Using chains of blow down of real De Concini - Procesi models, the author obtains a description of the ring structure of the homology of $Y_G$. By using this method, the author also proves that the homology of $\bar M_{0,n}(\Bbb R)$ has no odd torsion.
[Luca Chiantini (Siena)]

MSC 2000:: *14N20 Configurations of linear subspaces
14F25 Classical real and complex cohomology

Cited in: Zbl 1232.14038 Zbl 1206.14051

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