Arrangements of Hyperplanes

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Springer Science & Business Media, 2013年3月9日 - 325页
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.
 

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目录

Introduction
1
Combinatorics 23
22
Algebras
59
Free Arrangements
99
Topology
157
Reflection Arrangements
215
A Some Commutative Algebra 271
270
Basic Derivations
279
Exceptional Groups of Rank 2
280
The Coexponents
286
Orbit Types
289
ThreeDimensional Restrictions
301
References
303
Index
315
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