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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 $M/\Bbb{R}^+$ 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 [{\it R. MacPherson} and {\it C. Procesi}, Sel. Math., New Ser. 4, No. 1, 125--139 (1998; Zbl 0934.32014)].

##### MSC:
 32S22 Relations with arrangements of hyperplanes 58A35 Stratified sets (global analysis)
##### Keywords:
arrangements; stratified sets
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