Arrangements of HyperplanesSpringer-Verlag, 1992 - 325页 |
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第168页
... arrangements , but arrangements of arbitrary affine subspaces . In this setting , complex arrangements are just special cases of real arrangements . See also related work of Gelfand and Rybnikov [ 88 ] , and Björner and Ziegler [ 34 ] ...
... arrangements , but arrangements of arbitrary affine subspaces . In this setting , complex arrangements are just special cases of real arrangements . See also related work of Gelfand and Rybnikov [ 88 ] , and Björner and Ziegler [ 34 ] ...
第173页
... Real Arrangements We turn to the special case of the complexification of a real arrangement . We show first that it suffices to consider central arrangements . Suppose A is a complex hyperplane arrangement . If A is not central , then ...
... Real Arrangements We turn to the special case of the complexification of a real arrangement . We show first that it suffices to consider central arrangements . Suppose A is a complex hyperplane arrangement . If A is not central , then ...
第178页
... real arrangement , a presentation of π1 ( M ) was obtained by Randell [ 189 ] and Salvetti [ 203 , 204 ] . Their main result asserts that a presentation may be obtained from the underlying real arrangement of A , which we refer to as ...
... real arrangement , a presentation of π1 ( M ) was obtained by Randell [ 189 ] and Salvetti [ 203 , 204 ] . Their main result asserts that a presentation may be obtained from the underlying real arrangement of A , which we refer to as ...
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A₁ affine arrangement algebra A(A arrangement and let assume b₁ basic derivations basic invariants basis for D(A braid arrangement broken circuit central arrangement chain complex choose cohomology complement complex reflection groups complexification compute Corollary Coxeter group defining polynomial Definition deformation retraction degree denote dependent exact sequence Example exterior algebra exterior product fiber finite follows from Lemma follows from Proposition follows from Theorem formula free arrangement free with exp G-orbit graded K-module graph H₁ H₂ homogeneous homotopy type hyperplanes inductively free integers irreducible isomorphism K-algebra ker(x l-arrangement lattice Lemma Let G linear linearly independent matrix maximal element Möbius function modular elements module N¹(A nonempty Note Orbits Poincaré polynomial poset Proof prove real arrangement Recall reflection arrangement restriction result Saito's criterion 4.19 Section Shephard groups simplicial subset subspace supersolvable supersolvable arrangement Suppose surjective vertex w₁ write x-independent