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Real structures of models of arrangements. (English) Zbl 1076.52005

The author continues previous work, constructing and studying models of real subspace arrangements. Like the models of De Concini and Procesi for complex subspace arrangements, these are constructed in order to obtain information about invariants of the complement of the union of the subspaces. They are derived from combinatorial structures, called “building sets”, obtained from a finite partially ordered set of subspaces which is determined by the arrangement. There are usually many building sets associated with an arrangement, each giving rise to a model. This paper studies two real structures associated with the model. The first is essentially the real part of the De Concini-Procesi complex model. The second, which arises when the arrangement is a Coxeter arrangement, is an “extension” of the model to a convex set, the face lattice of which generalizes in a way the “Kapranov permutoassociahedron”.

MSC:

52C35 Arrangements of points, flats, hyperplanes (aspects of discrete geometry)
14E15 Global theory and resolution of singularities (algebro-geometric aspects)
32S22 Relations with arrangements of hyperplanes
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