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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共有 28 个结果,这是第 1-5 个
第ix页
... Poincaré Polynomial 222 23 23 23 26 28 30 32 32 34 35 38 42 Examples 42 The Deletion - Restriction Theorem 46 Supersolvable Arrangements Nice Partitions Counting Functions 48 55 50 51 2.4 Graphic Arrangements Definitions . Deletion ...
... Poincaré Polynomial 222 23 23 23 26 28 30 32 32 34 35 38 42 Examples 42 The Deletion - Restriction Theorem 46 Supersolvable Arrangements Nice Partitions Counting Functions 48 55 50 51 2.4 Graphic Arrangements Definitions . Deletion ...
第2页
... Poincaré polynomial . In 1969 , V. I. Arnold [ 6 ] proved the beautiful formula ( 1 ) Poin ( M , t ) = ( 1 + t ) ( 1 + 2t ) · · · ( 1 + ( l − 1 ) t ) = in connection with his work on Hilbert's 13th problem . He also constructed a ...
... Poincaré polynomial . In 1969 , V. I. Arnold [ 6 ] proved the beautiful formula ( 1 ) Poin ( M , t ) = ( 1 + t ) ( 1 + 2t ) · · · ( 1 + ( l − 1 ) t ) = in connection with his work on Hilbert's 13th problem . He also constructed a ...
第4页
... Poincaré polynomial . It follows from the definition that for the empty arrangement ( A , t ) = 1. He proved a result about the characteristic polynomial , which amounts to the following re- cursion for the Poincaré polynomial : π ( A ...
... Poincaré polynomial . It follows from the definition that for the empty arrangement ( A , t ) = 1. He proved a result about the characteristic polynomial , which amounts to the following re- cursion for the Poincaré polynomial : π ( A ...
第6页
... Poincaré polynomial of the complement of an arbitrary complex arrange- ment : ( 5 ) Poin ( M ( A ) , t ) = π ( A , t ) . Thus the Betti numbers of the complement depend only on the lattice of inter- sections of the hyperplanes . I ...
... Poincaré polynomial of the complement of an arbitrary complex arrange- ment : ( 5 ) Poin ( M ( A ) , t ) = π ( A , t ) . Thus the Betti numbers of the complement depend only on the lattice of inter- sections of the hyperplanes . I ...
第17页
... Poincaré polynomial of A , π ( A , t ) , which is related to another combinatorial function called the characteristic polynomial . We show that if cA is the cone over the affine arrangement A , then ( 1 ) π ( сА , t ) = ( 1 + t ) π ( A ...
... Poincaré polynomial of A , π ( A , t ) , which is related to another combinatorial function called the characteristic polynomial . We show that if cA is the cone over the affine arrangement A , then ( 1 ) π ( сА , t ) = ( 1 + t ) π ( A ...
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