Arrangements of HyperplanesSpringer 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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第vii页
... results . Their study combines methods from many areas of mathematics and reveals unexpected connections . The idea ... resulting lecture notes provided a core for the present work . Also in 1988 , H. Terao gave a course on arrangements ...
... results . Their study combines methods from many areas of mathematics and reveals unexpected connections . The idea ... resulting lecture notes provided a core for the present work . Also in 1988 , H. Terao gave a course on arrangements ...
第3页
... results captured an essential topological feature of arrangements . une famille finie quelconque d'hyperplans affines complexes Vi , i Є I , dans un espace affine complexe V. Pour calculer le p - iéme groupe de cohomologie , 0 ≤ p ≤ n ...
... results captured an essential topological feature of arrangements . une famille finie quelconque d'hyperplans affines complexes Vi , i Є I , dans un espace affine complexe V. Pour calculer le p - iéme groupe de cohomologie , 0 ≤ p ≤ n ...
第4页
... result was obtained independently by M. Las Vergnas [ 136 ] . Let A be an arrangement and let HЄ A be a hyperplane . Then A ' A \ { H } is called the deleted arrangement . The arrangement in H defined by A " = { K ^ H | K € A ' } is ...
... result was obtained independently by M. Las Vergnas [ 136 ] . Let A be an arrangement and let HЄ A be a hyperplane . Then A ' A \ { H } is called the deleted arrangement . The arrangement in H defined by A " = { K ^ H | K € A ' } is ...
第5页
... in 1980. P. Orlik and L. Solomon [ 171 ] used combinatorial methods to study the complement M ( A ) of a complex hyperplane arrangement A. They used Brieskorn's results to compute 1.1 Introduction 5 Topology The Complement M(A)
... in 1980. P. Orlik and L. Solomon [ 171 ] used combinatorial methods to study the complement M ( A ) of a complex hyperplane arrangement A. They used Brieskorn's results to compute 1.1 Introduction 5 Topology The Complement M(A)
第6页
Peter Orlik, Hiroaki Terao. complex hyperplane arrangement A. They used Brieskorn's results to compute the Poincaré polynomial of the complement of an arbitrary complex arrange- ment : ( 5 ) Poin ( M ( A ) , t ) = π ( A , t ) . Thus the ...
Peter Orlik, Hiroaki Terao. complex hyperplane arrangement A. They used Brieskorn's results to compute the Poincaré polynomial of the complement of an arbitrary complex arrange- ment : ( 5 ) Poin ( M ( A ) , t ) = π ( A , t ) . Thus the ...
目录
1 | |
4 | |
15 | |
22 | |
Examples | 30 |
Algebras | 59 |
The Injective Map AAx AA | 65 |
Supersolvable Arrangements | 80 |
115 | 204 |
Reflection Arrangements | 215 |
A Some Commutative Algebra 271 | 270 |
B Basic Derivations | 279 |
Orbit Types | 289 |
ThreeDimensional Restrictions | 301 |
164 | 310 |
Index | 315 |
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常见术语和短语
A₁ affine arrangement algebra A(A arrangement and let assume b₁ basic derivations basic invariants basis for D(A bijection braid arrangement broken circuit called central arrangement choose cohomology complement complex reflection groups complexification compute Corollary Coxeter group defining polynomial Definition deformation retraction degree denote exact sequence Example exterior product fiber finite follows from Lemma follows from Proposition follows from Theorem formula free arrangement free with exp fundamental group G-orbit graph H₁ H₂ homogeneous homotopy type hyperplane arrangement inductively free integers irreducible isomorphism ker(x l-arrangement lattice Lemma Let G linear linearly independent Math matrix maximal element Möbius function modular elements nonempty Note Orbits Poincaré polynomial poset Proof prove real arrangement Recall reflection arrangement restriction result Section set of basic Shephard groups simplicial subset subspace supersolvable Suppose surjective topological unitary reflection group vertex w₁ write