Arrangements of Hyperplanes / Edition 1

by Peter Orlik, Hiroaki Terao

Overview

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 among the different aspects of the subject. Its main purpose is to lay the foundations of 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 completegenerality. The text provides the advanced graduate student entry into a 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.

Product Details

ISBN-13:	9783642081378
Publisher:	Springer Berlin Heidelberg
Publication date:	12/15/2010
Series:	Grundlehren der mathematischen Wissenschaften , #300
Edition description:	Softcover reprint of hardcover 1st ed. 1992
Pages:	325
Product dimensions:	6.10(w) x 9.25(h) x 0.24(d)

Table of Contents

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.