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. |
在该图书中搜索
共有 91 个结果,这是第 1-5 个
第v页
... Arrangements of hyperplanes / Peter Orlik , Hiroaki Terao . p . cm . ( Grundlehren der mathematischen Wissenschaften ; 300 ) Includes bibliographical references and ... free paper To our parents Preface An arrangement of hyperplanes is a.
... Arrangements of hyperplanes / Peter Orlik , Hiroaki Terao . p . cm . ( Grundlehren der mathematischen Wissenschaften ; 300 ) Includes bibliographical references and ... free paper To our parents Preface An arrangement of hyperplanes is a.
第vii页
Peter Orlik, Hiroaki Terao. Preface An arrangement of hyperplanes is a finite collection of codimension one affine subspaces in a finite dimensional vector space . In this book we study arrange ... free arrangements in the fall of 1982. The ...
Peter Orlik, Hiroaki Terao. Preface An arrangement of hyperplanes is a finite collection of codimension one affine subspaces in a finite dimensional vector space . In this book we study arrange ... free arrangements in the fall of 1982. The ...
第xii页
... Arrangements Basic Properties . Examples . Relative Invariants Jacobian and Discriminant Classification 6.3 Free Arrangements Invariant Theory The Hessian . 216 218 219 222 · 223 • 223 225 228 229 231 232 232 234 DR ( 8 ) Is Free 235 ...
... Arrangements Basic Properties . Examples . Relative Invariants Jacobian and Discriminant Classification 6.3 Free Arrangements Invariant Theory The Hessian . 216 218 219 222 · 223 • 223 225 228 229 231 232 232 234 DR ( 8 ) Is Free 235 ...
第xiv页
... Free but not inductively free 122 4.2 Subdivision of 42 x I. 137 4.3 Folkman complexes for Q = xyz ( x + y ) ( x + y − z ) . 138 4.4 Complexes for the Boolean arrangement 139 4.5 ( A , t ) factors , but A is not free . 155 5.1 A braid ...
... Free but not inductively free 122 4.2 Subdivision of 42 x I. 137 4.3 Folkman complexes for Q = xyz ( x + y ) ( x + y − z ) . 138 4.4 Complexes for the Boolean arrangement 139 4.5 ( A , t ) factors , but A is not free . 155 5.1 A braid ...
第1页
... Free Jamison , Pittsburgh . [ ibid pp . 564-5 ] Since n straight lines can divide a plane into ( n2 + n + 2 ) / 2 areas , the ( n + 1 ) st plane can be divided by the first n planes into that number of areas . For each of these areas ...
... Free Jamison , Pittsburgh . [ ibid pp . 564-5 ] Since n straight lines can divide a plane into ( n2 + n + 2 ) / 2 areas , the ( n + 1 ) st plane can be divided by the first n planes into that number of areas . For each of these areas ...
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 |
其他版本 - 查看全部
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