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Models for real subspace arrangements and stratified manifolds. (English) Zbl 1068.32020

Consider a central plane arrangement in a vector space and let M denote its complement. In the first part of the paper, the author constructs certain compactifications of M/ + by embedding it in products of spheres. He shows that these compactifications are manifolds with corners and describes their boundaries. In the second part of the paper, the author describes a generalization of the previous procedure in terms of a sequence of blowups of stratified manifolds along strata.

This part of the paper is a real version of a procedure described in [R. MacPherson and C. Procesi, Sel. Math., New Ser. 4, No. 1, 125–139 (1998; Zbl 0934.32014)].

MSC:
32S22Relations with arrangements of hyperplanes
58A35Stratified sets (global analysis)