Arrangements of hyperplanes:
Gespeichert in:
| Hauptverfasser: | , |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Berlin u.a.
Springer
1992
|
| Schriftenreihe: | Grundlehren der mathematischen Wissenschaften
300 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | XVIII, 325 S. graph. Darst. |
| ISBN: | 3540552596 0387552596 |
Internformat
MARC
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| 100 | 1 | |a Orlik, Peter |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Arrangements of hyperplanes |c Peter Orlik ; Hiroaki Terao |
| 264 | 1 | |a Berlin u.a. |b Springer |c 1992 | |
| 300 | |a XVIII, 325 S. |b graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
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| 650 | 7 | |a Géométrie combinatoire |2 ram | |
| 650 | 4 | |a Hyperplans | |
| 650 | 7 | |a Problèmes combinatoires d'énumération |2 ram | |
| 650 | 7 | |a Treillis, théorie des |2 ram | |
| 650 | 4 | |a Combinatorial enumeration problems | |
| 650 | 4 | |a Combinatorial geometry | |
| 650 | 4 | |a Lattice theory | |
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Datensatz im Suchindex
| _version_ | 1804119707022786560 |
|---|---|
| adam_text | Table of Contents
1. Introduction 1
1.1 Introduction 1
History 1
Recent Advances 8
1.2 Definitions and Examples 10
Examples 11
Basic Constructions 13
The Module of ^ Derivations 15
The Complement of a Complex Arrangement 16
Reflection Arrangements 16
1.3 Outline 17
Combinatorics 17
Algebras 17
The Module of ^ Derivations 18
Topology 19
Reflection Arrangements 20
2. Combinatorics 23
2.1 The Poset L{A) 23
Definitions 23
Examples 26
Oriented Matroids 28
Supersolvable Arrangements 30
2.2 The Mobius Function 32
The Mobius Function 32
Mobius Inversion 34
The Function fi(X) 35
Historical Notes 38
2.3 The Poincare Polynomial 42
Examples 42
The Deletion Restriction Theorem 46
Supersolvable Arrangements 48
Nice Partitions 50
Counting Functions 51
X Table of Contents
2.4 Graphic Arrangements 52
Definitions 52
Deletion Contraction 54
Acyclic Orientations 57
3. Algebras 59
3.1 A(A) for Central Arrangements 60
Construction of A(A) 60
An Acyclic Complex 62
The Structure of A{A) 63
The Injective Map A(AX) A(A) 65
The Broken Circuit Basis 67
3.2 A(A) for Affine Arrangements 70
Construction of A(A) 70
The Broken Circuit Basis 72
Deletion and Restriction 74
The Structure of A{A) 77
^ equivalence 78
3.3 Algebra Factorizations 79
Supersolvable Arrangements 80
Nice Partitions of Central Arrangements 82
Nice Partitions of Affine Arrangements 85
3.4 The Algebra B(A) 86
The Shuffle Product 86
The Algebra B(A) 88
The Isomorphism of B and A 89
3.5 Differential Forms 92
The de Rham Complex 92
The Algebra R(A) 93
Deletion and Restriction 95
The Isomorphism of R and A 97
4. Free Arrangements 99
4.1 The Module D(A) 100
Derivations 100
Basic Properties 102
4.2 Free Arrangements 104
Saito s Criterion 104
Exponents 107
Examples Ill
4.3 The Addition Deletion Theorem 113
Basis Extension 114
The Map from D(A) to D{A ) 115
The Addition Deletion Theorem 117
Inductively Free Arrangements 119
Supersolvable Arrangements 121
Table of Contents XI
Factorization Theorem 122
4.4 The Modules Q (A) 123
Definition of QP(A) 124
Basic Properties of QP(A) 124
The Acyclic Complex {fl{A),d) 133
The 77 Complex {fl{A),dh) 133
4.5 Lattice Homology 135
The Order Complex 136
The Folkman Complex 137
The Homology Groups 140
The Homotopy Type 141
Whitney Homology 142
Connection with the Folkman Complex 144
4.6 The Characteristic Polynomial 145
The Order Complex with Functors 145
Local Functors 147
The Homology HP(A,F) 148
The Polynomial {A,x,t) 150
The Factorization Theorem 154
5. Topology 157
5.1 The Complement M(A) 158
K(n, 1) Arrangements 159
Free Arrangements 163
Generic Arrangements 164
Deformation 166
Arnold s Conjectures 167
5.2 The Homotopy Type of M(A) 168
Real Arrangements 168
The Homotopy Type 171
Complexified Real Arrangements 173
Salvetti s Complex 175
The Homotopy Equivalence 176
5.3 The Fundamental Group 177
Admissible Graphs 179
Arvola s Presentation 184
5.4 The Cohomology of M{A) 190
The Thom Isomorphism 191
Brieskorn s Lemma 195
5.5 The Fibration Theorem 196
Horizontal Subspaces 197
Good Subspaces 198
Good Lines 199
5.6 Related Research 202
Minimal Models 202
XII Table of Contents
Discriminantal Arrangements 205
Alexander Duality 207
The Milnor Fiber of a Generic Arrangement 209
Arrangements of Subspaces 211
6. Reflection Arrangements 215
6.1 Equivariant Theory 216
The Action of G 216
Matrices 218
Character Formulas 219
Topological Interpretation 222
6.2 Reflection Arrangements 223
Basic Properties 223
Examples 225
Relative Invariants 228
Jacobian and Discriminant 229
Classification 231
6.3 Free Arrangements 232
Invariant Theory 232
The Hessian 234
DR(6) Is Free 235
D{A) Is Free 237
The Discriminant Matrix 238
A Character Formula 241
6.4 The Structure of L(A) 243
The Symmetric Group 243
The Full Monomial Group 244
The Monomial Group G(r, r,£) 247
The Exceptional Groups 251
6.5 Restrictions 254
The Cardinality of A 254
AH Is Free In Coxeter Arrangements 256
6.6 Topology 259
Stratification of the Discriminant 259
Shephard Groups 265
The K(ir, 1) Problem 267
A. Some Commutative Algebra 271
A.I Free Modules 271
A.2 Krull Dimension 272
A.3 Graded Modules 274
A.4 Associated Primes and Regular Sequences 276
Table of Contents XIII
B. Basic Derivations 279
B.I The Infinite Families 279
B.2 Exceptional Groups of Rank 2 280
B.3 Exceptional Groups of Rank 3 280
B.4 The Coexponents 286
C. Orbit Types 289
D. Three Dimensional Restrictions 301
References 303
Index 315
Index of Symbols 323
|
| any_adam_object | 1 |
| author | Orlik, Peter Terao, Hiroaki |
| author_facet | Orlik, Peter Terao, Hiroaki |
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| building | Verbundindex |
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| callnumber-subject | QA - Mathematics |
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| classification_tum | MAT 146f |
| ctrlnum | (OCoLC)25409160 (DE-599)BVBBV005492012 |
| dewey-full | 516/.13 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 516 - Geometry |
| dewey-raw | 516/.13 |
| dewey-search | 516/.13 |
| dewey-sort | 3516 213 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| format | Book |
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| id | DE-604.BV005492012 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T16:30:28Z |
| institution | BVB |
| isbn | 3540552596 0387552596 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-003439632 |
| oclc_num | 25409160 |
| open_access_boolean | |
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| physical | XVIII, 325 S. graph. Darst. |
| publishDate | 1992 |
| publishDateSearch | 1992 |
| publishDateSort | 1992 |
| publisher | Springer |
| record_format | marc |
| series | Grundlehren der mathematischen Wissenschaften |
| series2 | Grundlehren der mathematischen Wissenschaften |
| spelling | Orlik, Peter Verfasser aut Arrangements of hyperplanes Peter Orlik ; Hiroaki Terao Berlin u.a. Springer 1992 XVIII, 325 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Grundlehren der mathematischen Wissenschaften 300 Géométrie combinatoire Géométrie combinatoire ram Hyperplans Problèmes combinatoires d'énumération ram Treillis, théorie des ram Combinatorial enumeration problems Combinatorial geometry Lattice theory Anordnung Mathematik (DE-588)4211643-0 gnd rswk-swf Hyperebene (DE-588)4161050-7 gnd rswk-swf Anordnung (DE-588)4142560-1 gnd rswk-swf Gittertheorie (DE-588)4157394-8 gnd rswk-swf Kombinatorische Geometrie (DE-588)4140733-7 gnd rswk-swf Hyperfläche (DE-588)4161054-4 gnd rswk-swf Hyperebene (DE-588)4161050-7 s Anordnung (DE-588)4142560-1 s DE-604 Kombinatorische Geometrie (DE-588)4140733-7 s Gittertheorie (DE-588)4157394-8 s Anordnung Mathematik (DE-588)4211643-0 s Hyperfläche (DE-588)4161054-4 s Terao, Hiroaki Verfasser aut Grundlehren der mathematischen Wissenschaften 300 (DE-604)BV000000395 300 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=003439632&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Orlik, Peter Terao, Hiroaki Arrangements of hyperplanes Grundlehren der mathematischen Wissenschaften Géométrie combinatoire Géométrie combinatoire ram Hyperplans Problèmes combinatoires d'énumération ram Treillis, théorie des ram Combinatorial enumeration problems Combinatorial geometry Lattice theory Anordnung Mathematik (DE-588)4211643-0 gnd Hyperebene (DE-588)4161050-7 gnd Anordnung (DE-588)4142560-1 gnd Gittertheorie (DE-588)4157394-8 gnd Kombinatorische Geometrie (DE-588)4140733-7 gnd Hyperfläche (DE-588)4161054-4 gnd |
| subject_GND | (DE-588)4211643-0 (DE-588)4161050-7 (DE-588)4142560-1 (DE-588)4157394-8 (DE-588)4140733-7 (DE-588)4161054-4 |
| title | Arrangements of hyperplanes |
| title_auth | Arrangements of hyperplanes |
| title_exact_search | Arrangements of hyperplanes |
| title_full | Arrangements of hyperplanes Peter Orlik ; Hiroaki Terao |
| title_fullStr | Arrangements of hyperplanes Peter Orlik ; Hiroaki Terao |
| title_full_unstemmed | Arrangements of hyperplanes Peter Orlik ; Hiroaki Terao |
| title_short | Arrangements of hyperplanes |
| title_sort | arrangements of hyperplanes |
| topic | Géométrie combinatoire Géométrie combinatoire ram Hyperplans Problèmes combinatoires d'énumération ram Treillis, théorie des ram Combinatorial enumeration problems Combinatorial geometry Lattice theory Anordnung Mathematik (DE-588)4211643-0 gnd Hyperebene (DE-588)4161050-7 gnd Anordnung (DE-588)4142560-1 gnd Gittertheorie (DE-588)4157394-8 gnd Kombinatorische Geometrie (DE-588)4140733-7 gnd Hyperfläche (DE-588)4161054-4 gnd |
| topic_facet | Géométrie combinatoire Hyperplans Problèmes combinatoires d'énumération Treillis, théorie des Combinatorial enumeration problems Combinatorial geometry Lattice theory Anordnung Mathematik Hyperebene Anordnung Gittertheorie Kombinatorische Geometrie Hyperfläche |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=003439632&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV000000395 |
| work_keys_str_mv | AT orlikpeter arrangementsofhyperplanes AT teraohiroaki arrangementsofhyperplanes |