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The homology of real subspace arrangements. (English) Zbl 1213.14102
Let V be a vector space and let G be a building set, i.e. a finite collection of subspaces of the dual V * , whose elements are indecomposable. The open set V- H i G H i has a natural emebdding in the product of the projective spaces (V/H i ). 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 M ¯ 0,n () of marked rational curves. Starting with a combinatorial description of the homology of V- H i G H i , it is possible to characterize the homology of M ¯ 0,n (). 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 M ¯ 0,n () has no odd torsion.

14N20Configurations and arrangements of linear subspaces
14F25Classical real and complex cohomology