Arrangements of Hyperplanes

324 pages, parution le 12/12/2001

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Résumé

An arrangement of hyperplanes is a finite collection of codimension one affine subspaces in a finite dimensional vector space. Arrangements have emerged independently as important objects in various fields of mathematics such as combinatorics, braids, configuration spaces, representation theory, reflection groups, singularity theory, and in computer science and physics.

This book is the first comprehensive study of the subject. It treats arrangements with methods from combinatorics, algebra, algebraic geometry, topology, and group actions. It emphasizes general techniques which illuminate the connections amongthe different aspects of the subject. Its main purpose is to lay the foundationsof the theory. Consequently, it is essentially self-contained and proofs are provided. Nevertheless, there are several new results here. In particular, many theorems that were previously known only for central arrangements are proved here for the first time in complete generality.

The text provides the advanced graduate student entry into a vital and active area of research. The working mathematician will find the book useful as a source of basic results of the theory, open problems, and a comprehensive bibliography of the subject.

Contents

Introduction
Combinatorics
Algebras
Free arrangements
Topology
Reflection arrangements
Some commutative algebra
Basic derivations
Orbit types
Three-dimensional restrictions
References
Index