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 30 个结果,这是第 1-5 个
第2页
... field of arrangements of hyperplanes , which I expect to become increasingly popular during the next few years ... the theory of arrangements may be developed , much like topology , in rectilinear or curved versions as well as in ...
... field of arrangements of hyperplanes , which I expect to become increasingly popular during the next few years ... the theory of arrangements may be developed , much like topology , in rectilinear or curved versions as well as in ...
第7页
... fields and logarithmic differ- ential forms on a hypersurface was initiated by K. Saito [ 199 , 201 ] . He defined free hypersurfaces in the analytic category . Arrangements represent a special case . Here the hypersurface is the union ...
... fields and logarithmic differ- ential forms on a hypersurface was initiated by K. Saito [ 199 , 201 ] . He defined free hypersurfaces in the analytic category . Arrangements represent a special case . Here the hypersurface is the union ...
第9页
... field of real numbers , it is known that any S - G configuration is linear . Over the field of complex numbers there are well- known examples of nonlinear S - G configurations ( e . g . the nine inflection points of a nonsingular cubic ...
... field of real numbers , it is known that any S - G configuration is linear . Over the field of complex numbers there are well- known examples of nonlinear S - G configurations ( e . g . the nine inflection points of a nonsingular cubic ...
第10页
... field of characteristic three , while the other is over characteristic not equal to three . Conjecture ( ii ) is still open for arrangements defined over the same field . S. Yuzvinsky [ 254 , 255 ] gave interesting necessary conditions ...
... field of characteristic three , while the other is over characteristic not equal to three . Conjecture ( ii ) is still open for arrangements defined over the same field . S. Yuzvinsky [ 254 , 255 ] gave interesting necessary conditions ...
第11页
... field . We call A an l - arrangement when we want to emphasize the dimension of V. Let denote the empty l - arrangement . Let V * be the dual space of V , the space of linear forms on V. Let S = S ( V * ) be the symmetric algebra of V ...
... field . We call A an l - arrangement when we want to emphasize the dimension of V. Let denote the empty l - arrangement . Let V * be the dual space of V , the space of linear forms on V. Let S = S ( V * ) be the symmetric algebra of V ...
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