Arrangements of HyperplanesSpringer-Verlag, 1992 - 325页 |
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第116页
... assume that D ( A ) has a basis { 01 , ... , 0-1 , Pi , Pi + 1 , ... , Pe } where 1 ≤ i ≤l . Thus if i = 1 , the two bases have no common element . Let dj pdegøj , and assume dide and d1 ≤ ... < di - 1 ≤ ei < ... < e . Note that 0 ...
... assume that D ( A ) has a basis { 01 , ... , 0-1 , Pi , Pi + 1 , ... , Pe } where 1 ≤ i ≤l . Thus if i = 1 , the two bases have no common element . Let dj pdegøj , and assume dide and d1 ≤ ... < di - 1 ≤ ei < ... < e . Note that 0 ...
第117页
... Assume that A " is free with exp A " = { b1 , ... , be - 1 } where b1 ... bk - 1 < bk ≤ · · · ≤ · ≤be - 1 . = bj for 1 ≤ j ≤ k − 1 and -- Suppose 01 , ... , 0k € D ( A ) such that pdegėj pdegok bk . There exists p with 1 ≤ p ≤ k ...
... Assume that A " is free with exp A " = { b1 , ... , be - 1 } where b1 ... bk - 1 < bk ≤ · · · ≤ · ≤be - 1 . = bj for 1 ≤ j ≤ k − 1 and -- Suppose 01 , ... , 0k € D ( A ) such that pdegėj pdegok bk . There exists p with 1 ≤ p ≤ k ...
第118页
... assume that 0 , E aoD ( A ' ) . It follows from Saito's criterion 4.19 that is a basis for D ( A ' ) . θε 01 , ... , Op - 1 , 2 , Op + 1 , , Op + 1 , ... , Ol απ Theorem 4.50 ( Addition ) If A ' and A " are free and exp A " C exp A ...
... assume that 0 , E aoD ( A ' ) . It follows from Saito's criterion 4.19 that is a basis for D ( A ' ) . θε 01 , ... , Op - 1 , 2 , Op + 1 , , Op + 1 , ... , Ol απ Theorem 4.50 ( Addition ) If A ' and A " are free and exp A " C exp A ...
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常见术语和短语
A₁ affine arrangement algebra A(A arrangement and let arrangements of hyperplanes assume b₁ basic invariants basis for D(A braid arrangement Brieskorn broken circuit central arrangement chain complex cohomology complement complex reflection groups complexification compute construction Corollary Coxeter group defining polynomial Definition deformation retraction denote dependent exact sequence Example exterior algebra fiber finite follows from Lemma follows from Proposition formula free arrangement free with exp graded K-module graph H₁ H₂ homogeneous homology homotopy type hyperplane arrangement hyperplanes inductively free integers irreducible isomorphism K-algebra ker(x l-arrangement lattice Lemma Let G linear linearly independent Math matrix maximal element Möbius function modular elements module nonempty Note Orbits Poincaré polynomial poset Proof prove real arrangement Recall reflection arrangement restriction result Section Shephard groups simplicial space subset subspace supersolvable supersolvable arrangement Suppose surjective topological vertex vertices w₁ write x-independent