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11页
... arrangement Þ , is central . When we want to emphasize that an arrangement can be either centered or centerless we call it affine . Definition 1.4 A projective arrangement is a finite set of projective hyper- planes in projective space ...
... arrangement Þ , is central . When we want to emphasize that an arrangement can be either centered or centerless we call it affine . Definition 1.4 A projective arrangement is a finite set of projective hyper- planes in projective space ...
第12页
... central 3 - arrangement de- fined by Q ( A ) = xyz ( x − y ) ( x + y ) ( x − z ) ( x + z ) ( y − z ) ( y + z ) . These nine planes intersect in lines which are axes of rotational symmetry for the cube . The group of symmetries of the ...
... central 3 - arrangement de- fined by Q ( A ) = xyz ( x − y ) ( x + y ) ( x − z ) ( x + z ) ( y − z ) ( y + z ) . These nine planes intersect in lines which are axes of rotational symmetry for the cube . The group of symmetries of the ...
第13页
... arrangement defined by Q ( A ) = x1X2 xl . This is the arrangement of the coordinate hyperplanes in IR ' . = Example ... central arrangement in V consisting of all hyperplanes through the origin . Basic Constructions Definition 1.11 Let ...
... arrangement defined by Q ( A ) = x1X2 xl . This is the arrangement of the coordinate hyperplanes in IR ' . = Example ... central arrangement in V consisting of all hyperplanes through the origin . Basic Constructions Definition 1.11 Let ...
第14页
... arrangements and Ho the distinguished hyperplane . The method of coning is another basic construction . It allows for comparing affine and central arrangements . = Definition 1.15 An affine l - arrangement A defined by Q ( A ) E S gives ...
... arrangements and Ho the distinguished hyperplane . The method of coning is another basic construction . It allows for comparing affine and central arrangements . = Definition 1.15 An affine l - arrangement A defined by Q ( A ) E S gives ...
第15页
... central arrangement A then removing the image of Ko , the hyperplane at infinity , and identifying its complement with affine space . There are two sets of fundamental interest in the study of arrangements : the variety of A and the ...
... central arrangement A then removing the image of Ko , the hyperplane at infinity , and identifying its complement with affine space . There are two sets of fundamental interest in the study of arrangements : the variety of A and 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