Arrangements of HyperplanesSpringer-Verlag, 1992 - 325页 |
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第78页
... proof is the same as the proof of the central version , Corollary 3.27 . Corollary 3.73 will be used in Theorem 5.91 to give an elementary proof of Brieskorn's Lemma . Corollary 3.73 Let A be an affine arrangement . Then Ap = → XEL ...
... proof is the same as the proof of the central version , Corollary 3.27 . Corollary 3.73 will be used in Theorem 5.91 to give an elementary proof of Brieskorn's Lemma . Corollary 3.73 Let A be an affine arrangement . Then Ap = → XEL ...
第90页
... Proof . If ns = 0 , then ( es ) = bs = 0. If S is dependent , then des = 0 , so des Є kery . Thus IC kery and induces a surjective map : A → B such that as = bs . Since is an algebra homomorphism , so is = τψες Tbs 0 0 . Lemma 3.108 If ...
... Proof . If ns = 0 , then ( es ) = bs = 0. If S is dependent , then des = 0 , so des Є kery . Thus IC kery and induces a surjective map : A → B such that as = bs . Since is an algebra homomorphism , so is = τψες Tbs 0 0 . Lemma 3.108 If ...
第198页
... Proof . We have = L. Note that the p ( X ) | M ( A / Y ) = 0 ↔ p ( X ) ≤ p ( H ) for some HЄ Ay X + YCH for some HЄ Ay + X + Y CH for some HЄ Ay + XAY # V . This completes the proof . Proposition 5.103 The following four conditions on ...
... Proof . We have = L. Note that the p ( X ) | M ( A / Y ) = 0 ↔ p ( X ) ≤ p ( H ) for some HЄ Ay X + YCH for some HЄ Ay + X + Y CH for some HЄ Ay + XAY # V . This completes the proof . Proposition 5.103 The following four conditions on ...
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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