Deformations of Coxeter hyperplane arrangements and their characteristic polynomials. (English) Zbl 0976.32016

Athanasiadis, Christos A.

Falk, Michael (ed.) et al., Arrangements - Tokyo 1998. Proceedings of a workshop on mathematics related to arrangements of hyperplanes, Tokyo, Japan, July 13-18, 1998. In honor of the 60th birthyear of Peter Orlik. Tokyo: Kinokuniya Company Ltd. Adv. Stud. Pure Math. 27, 1-26 (2000).

Let \({\mathcal A}\) be a Coxeter hyperplane arrangement, i.e. an arrangement of reflecting hyperplanes of an irreducible finite Coxeter group. A deformations of \({\mathcal A}\) is an affine arrangement such that the hyperplanes are parallel to some hyperplane of \({\mathcal A}\).
A survey about the work on deformation of Coxeter arrangements concerning the combinatorial and algebraic properties related to their characteristic polynomial is given.
For the entire collection see [Zbl 0952.00034].

Reviewer: Gerhard Pfister (Kaiserslautern)

MSC:

32S22	Relations with arrangements of hyperplanes
52C30	Planar arrangements of lines and pseudolines (aspects of discrete geometry)

Keywords:

Coxeter hyperplane arrangement; deformation; survey