Arrangements of HyperplanesSpringer-Verlag, 1992 - 325页 |
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第63页
... ideal I and return to the notation = JE . Definition 3.14 Let J = J ( A ) be the submodule of E spanned over K by all es such that SES is dependent . Lemma 3.15 J is an ideal of E and I = J + JJ . Proof . If TЄ S is dependent , then ( S ...
... ideal I and return to the notation = JE . Definition 3.14 Let J = J ( A ) be the submodule of E spanned over K by all es such that SES is dependent . Lemma 3.15 J is an ideal of E and I = J + JJ . Proof . If TЄ S is dependent , then ( S ...
第114页
... ideal D ( A ' ) αo is contained in ( ao , b ( A ) ) . Proof . Since D ( A ' ) is an S - module , D ( A ' ) ao is an ideal . Let X € A " and v ( X ) Є A ' . Let A'x Ax { Ho } . Then r ( Ax ) ≤ r ( Ax ) nonempty free arrangement . If we ...
... ideal D ( A ' ) αo is contained in ( ao , b ( A ) ) . Proof . Since D ( A ' ) is an S - module , D ( A ' ) ao is an ideal . Let X € A " and v ( X ) Є A ' . Let A'x Ax { Ho } . Then r ( Ax ) ≤ r ( Ax ) nonempty free arrangement . If we ...
第277页
... ideal whose length is equal to the Krull di- mension . A ring R is said to be Cohen - Macaulay if the locaization at every maximal ideal is Cohen - Macaulay . The following three results [ 153 , Thms . 17.7 , 17.6 , 17.4 ] are ...
... ideal whose length is equal to the Krull di- mension . A ring R is said to be Cohen - Macaulay if the locaization at every maximal ideal is Cohen - Macaulay . The following three results [ 153 , Thms . 17.7 , 17.6 , 17.4 ] are ...
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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