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

Gaiffi, Giovanni

Int. Math. Res. Not. 2003, No. 12, 627-656 (2003).

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

Reviewer: Pedro Ferreira dos Santos (Lisboa)

MSC:

32S22	Relations with arrangements of hyperplanes
58A35	Stratified sets

Keywords:

arrangements; stratified sets

Citations:

Zbl 0934.32014