Arrangements of HyperplanesSpringer Science & Business Media, 1992年8月6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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Peter Orlik, Hiroaki Terao. Table of Contents 1. Introduction 1.1 Introduction . History . . . Recent Advances 1.2 Definitions and Examples 1 1 8 10 Examples Basic Constructions . 11 13 The Module of A - Derivations The Complement of a ...
Peter Orlik, Hiroaki Terao. Table of Contents 1. Introduction 1.1 Introduction . History . . . Recent Advances 1.2 Definitions and Examples 1 1 8 10 Examples Basic Constructions . 11 13 The Module of A - Derivations The Complement of a ...
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... . 114 The Map from D ( A ) to D ( A " ) 115 The Addition - Deletion Theorem . Inductively Free Arrangements . Supersolvable Arrangements 117 119 121 Factorization Theorem 4.4 The Modules P ( A ) Definition X Table of Contents.
... . 114 The Map from D ( A ) to D ( A " ) 115 The Addition - Deletion Theorem . Inductively Free Arrangements . Supersolvable Arrangements 117 119 121 Factorization Theorem 4.4 The Modules P ( A ) Definition X Table of Contents.
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... Brieskorn's Lemma 5.5 The Fibration Theorem . Horizontal Subspaces Good Subspaces Good Lines 5.6 Related Research Minimal Models • Discriminantal Arrangements 205 Alexander Duality 207 The Milnor Fiber of Table of Contents XI.
... Brieskorn's Lemma 5.5 The Fibration Theorem . Horizontal Subspaces Good Subspaces Good Lines 5.6 Related Research Minimal Models • Discriminantal Arrangements 205 Alexander Duality 207 The Milnor Fiber of Table of Contents XI.
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... " 254 . 254 256 259 259 265 267 271 • 271 A.2 Krull Dimension . 272 A.3 Graded Modules . . 274 A.4 Associated Primes and Regular Sequences 276 B. Basic Derivations . B.1 The Infinite Families B.2 Exceptional XII Table of Contents.
... " 254 . 254 256 259 259 265 267 271 • 271 A.2 Krull Dimension . 272 A.3 Graded Modules . . 274 A.4 Associated Primes and Regular Sequences 276 B. Basic Derivations . B.1 The Infinite Families B.2 Exceptional XII Table of Contents.
目录
I | 1 |
II | 8 |
III | 10 |
IV | 11 |
V | 13 |
VI | 15 |
VII | 16 |
IX | 17 |
LXXXII | 144 |
LXXXIII | 145 |
LXXXV | 147 |
LXXXVI | 148 |
LXXXVII | 150 |
LXXXVIII | 154 |
LXXXIX | 157 |
XC | 158 |
X | 18 |
XI | 19 |
XII | 20 |
XIII | 23 |
XV | 26 |
XVI | 28 |
XVII | 30 |
XVIII | 32 |
XIX | 34 |
XX | 35 |
XXI | 38 |
XXII | 42 |
XXIV | 46 |
XXV | 48 |
XXVI | 50 |
XXVII | 51 |
XXVIII | 52 |
XXX | 54 |
XXXI | 57 |
XXXII | 59 |
XXXIII | 60 |
XXXV | 62 |
XXXVI | 63 |
XXXVII | 65 |
XXXVIII | 67 |
XXXIX | 70 |
XLI | 72 |
XLII | 74 |
XLIII | 77 |
XLIV | 78 |
XLV | 79 |
XLVI | 80 |
XLVII | 82 |
XLVIII | 85 |
XLIX | 86 |
LI | 88 |
LII | 89 |
LIII | 92 |
LV | 93 |
LVI | 95 |
LVII | 97 |
LVIII | 99 |
LIX | 100 |
LX | 102 |
LXI | 104 |
LXII | 107 |
LXIII | 111 |
LXIV | 113 |
LXV | 114 |
LXVI | 115 |
LXVII | 117 |
LXVIII | 119 |
LXIX | 121 |
LXX | 122 |
LXXI | 123 |
LXXII | 124 |
LXXIV | 133 |
LXXVI | 135 |
LXXVII | 136 |
LXXVIII | 137 |
LXXIX | 140 |
LXXX | 141 |
LXXXI | 142 |
XCI | 159 |
XCII | 163 |
XCIII | 164 |
XCIV | 166 |
XCV | 167 |
XCVI | 168 |
XCVIII | 171 |
XCIX | 173 |
C | 175 |
CI | 176 |
CII | 177 |
CIII | 179 |
CIV | 184 |
CV | 190 |
CVI | 191 |
CVII | 195 |
CVIII | 196 |
CIX | 197 |
CX | 198 |
CXI | 199 |
CXII | 202 |
CXIII | 205 |
CXIV | 207 |
CXV | 209 |
CXVI | 211 |
CXVII | 215 |
CXVIII | 216 |
CXIX | 218 |
CXX | 219 |
CXXI | 222 |
CXXII | 223 |
CXXIII | 225 |
CXXIV | 228 |
CXXV | 229 |
CXXVI | 231 |
CXXVII | 232 |
CXXVIII | 234 |
CXXIX | 235 |
CXXX | 237 |
CXXXI | 238 |
CXXXII | 241 |
CXXXIII | 243 |
CXXXV | 244 |
CXXXVI | 247 |
CXXXVII | 251 |
CXXXVIII | 254 |
CXXXIX | 256 |
CXL | 259 |
CXLII | 265 |
CXLIII | 267 |
CXLIV | 271 |
CXLVI | 272 |
CXLVII | 274 |
CXLVIII | 276 |
CXLIX | 279 |
CLI | 280 |
CLIII | 286 |
CLIV | 289 |
CLV | 301 |
303 | |
315 | |
323 | |
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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 derivations basic invariants basis for D(A braid arrangement broken circuit called central arrangement characteristic polynomial choose cohomology complement complex reflection groups complexification compute Corollary Coxeter group defining polynomial Definition deformation retraction degree denote Derg exact sequence Example fiber finite follows from Lemma follows from Proposition follows from Theorem formula free arrangement free with exp 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 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