# zbMATH — the first resource for mathematics

Combinatorial stratification of complex arrangements. (English) Zbl 0754.52003
An arrangement of complex hyperplanes of $$\mathbb{C}^ d$$ through the origin is encoded by certain combinatorial data in terms of complex signs, posets, matroids, and stratifications. The topology of such an arrangement and its complement is studied, in particular for its link in the sphere $$S^{2d-1}$$. Somehow, this corresponds to results by J. Milnor and E. Brieskorn on complex singularities. Especially it is shown that for $$d\geq 4$$ the link of an arrangement has the homotopy type of a wedge of spheres. Alexander duality provides a relation for the homology and cohomology. Finally, an outline is given for more general types of arrangements.

##### MSC:
 52C35 Arrangements of points, flats, hyperplanes (aspects of discrete geometry) 57N80 Stratifications in topological manifolds 05B35 Combinatorial aspects of matroids and geometric lattices 32S60 Stratifications; constructible sheaves; intersection cohomology (complex-analytic aspects)
Full Text: