Arrangements of Hyperplanes

1. Front Matter

   Pages I-XVIII

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2. Introduction

   • Peter Orlik, Hiroaki Terao

   Pages 1-21

3. Combinatorics

   • Peter Orlik, Hiroaki Terao

   Pages 23-58

4. Algebras

   • Peter Orlik, Hiroaki Terao

   Pages 59-98

5. Free Arrangements

   • Peter Orlik, Hiroaki Terao

   Pages 99-156

6. Topology

   • Peter Orlik, Hiroaki Terao

   Pages 157-213

7. Reflection Arrangements

   • Peter Orlik, Hiroaki Terao

   Pages 215-269

8. Some Commutative Algebra

   • Peter Orlik, Hiroaki Terao

   Pages 271-277

9. Basic Derivations

   • Peter Orlik, Hiroaki Terao

   Pages 279-288

10. Orbit Types

    • Peter Orlik, Hiroaki Terao

    Pages 289-300

11. Three-Dimensional Restrictions

    • Peter Orlik, Hiroaki Terao

    Pages 301-302

12. Back Matter

    Pages 303-325

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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.

• algebraic topology of manifolds
• geometric lattices
• reflection groups
• singularities
• singularity theory

• Department of Mathematics, University of Wisconsin, Madison, USA

  Peter Orlik, Hiroaki Terao

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