Arrangements of Hyperplanes

ISBN-13: 9783540552598 / Angielski / Twarda / 1992 / 325 str.

Peter Orlik; Hiroaki Terao

Opis

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 comprehensivestudy 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 among the different aspects of the subject. Its main purpose is to lay the foundations of the theory. Consequently, it is essentially self-containedand proofs are provided. Nevertheless, there are several new results here. In particular, many theorems that were previously knownonly for central arrangements are proved here for the first time in completegenerality. The text provides the advanced graduate student entry intoa vital and active area of research. The working mathematician will findthe book useful as a source of basic results of the theory, open problems, and a comprehensive bibliography of the subject.

Spis treści

1. Introduction.- 2. Combinatorics.- 3. Algebras.- 4. Free Arrangements.- 5. Topology.- 6. Reflection Arrangements.- A. Some Commutative Algebra.- B. Basic Derivations.- C. Orbit Types.- D. Three-Dimensional Restrictions.- References.- Index of Symbols.