Arrangements of Hyperplanes

  • Peter Orlik
  • Hiroaki Terao

Part of the Grundlehren der mathematischen Wissenschaften book series (GL, volume 300)

Table of contents

  1. Front Matter
    Pages I-XVIII
  2. Peter Orlik, Hiroaki Terao
    Pages 1-21
  3. Peter Orlik, Hiroaki Terao
    Pages 23-58
  4. Peter Orlik, Hiroaki Terao
    Pages 59-98
  5. Peter Orlik, Hiroaki Terao
    Pages 99-156
  6. Peter Orlik, Hiroaki Terao
    Pages 157-213
  7. Peter Orlik, Hiroaki Terao
    Pages 215-269
  8. Peter Orlik, Hiroaki Terao
    Pages 271-277
  9. Peter Orlik, Hiroaki Terao
    Pages 279-288
  10. Peter Orlik, Hiroaki Terao
    Pages 289-300
  11. Peter Orlik, Hiroaki Terao
    Pages 301-302
  12. Back Matter
    Pages 303-325

About this book

Introduction

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.

Keywords

algebraic topology of manifolds geometric lattices reflection groups singularities singularity theory

Authors and affiliations

  • Peter Orlik
    • 1
  • Hiroaki Terao
    • 1
  1. 1.Department of MathematicsUniversity of WisconsinMadisonUSA

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-662-02772-1
  • Copyright Information Springer-Verlag Berlin Heidelberg 1992
  • Publisher Name Springer, Berlin, Heidelberg
  • eBook Packages Springer Book Archive
  • Print ISBN 978-3-642-08137-8
  • Online ISBN 978-3-662-02772-1
  • Series Print ISSN 0072-7830
  • About this book