We will deal with two “hidden” real structures in the theory of models of subspace arrangements. Given a real subspace arrangement A and its complexification A_C, the first structure is a real De Concini-Procesi model that can be seen as the manifold Y_A of (canonical) real points inside the complex De Concini-Procesi model Y_{A_C}. We will study its combinatorial properties by describing it as a quotient of a real model with corners CY_A introduced in 2003. A second structure arises, on the contrary, as an “extension” of CY_A, when A is a Coxeter arrangement. We will “add faces” to CY_A and obtain a convex body (or even a polytope); this gives rise to an interesting new family of “realized” posets which includes for instance Kapranov's permutoassociahedra.
Real structures of models of arrangements
GAIFFI, GIOVANNI
2004-01-01
Abstract
We will deal with two “hidden” real structures in the theory of models of subspace arrangements. Given a real subspace arrangement A and its complexification A_C, the first structure is a real De Concini-Procesi model that can be seen as the manifold Y_A of (canonical) real points inside the complex De Concini-Procesi model Y_{A_C}. We will study its combinatorial properties by describing it as a quotient of a real model with corners CY_A introduced in 2003. A second structure arises, on the contrary, as an “extension” of CY_A, when A is a Coxeter arrangement. We will “add faces” to CY_A and obtain a convex body (or even a polytope); this gives rise to an interesting new family of “realized” posets which includes for instance Kapranov's permutoassociahedra.File | Dimensione | Formato | |
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Int. Math. Res. Not. IMRN 2004 Gaiffi.pdf
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