Models for real subspace arrangements and stratified manifolds

We consider a central subspace and half-space arrangement A in Euclidean vector space V, and let M(A) be its complement. We construct some compactifications for the C∞-manifold M(A)/ℝ+. They turn out to be C∞-manifolds with corners whose boundary is determined by simple combinatorial data. This generalizes a construction described by Kontsevich in his paper on deformation quantization of Poisson manifolds. Then, we extend the construction to more general objects, that is, stratified real manifolds whose stratification locally looks like the one induced by an arrangement of linear (half-) spaces. The models we obtain are again C∞-manifolds with corners equipped with a nice combinatorial description of the boundary.