Homogeneous spaces and equivariant embeddings:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Berlin [u.a.]
Springer
2011
|
| Ausgabe: | 1. ed. |
| Schriftenreihe: | Encyclopaedia of Mathematical Sciences
138 |
| Schlagworte: | |
| Online-Zugang: | Inhaltstext Inhaltsverzeichnis |
| Beschreibung: | XXI, 253 S. graph. Darst. |
| ISBN: | 3642183980 9783642183980 |
Internformat
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| 100 | 1 | |a Timašev, Dmitrij A. |d 1971- |e Verfasser |0 (DE-588)1012190994 |4 aut | |
| 245 | 1 | 0 | |a Homogeneous spaces and equivariant embeddings |c Dmitry A. Timashev |
| 250 | |a 1. ed. | ||
| 264 | 1 | |a Berlin [u.a.] |b Springer |c 2011 | |
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| 490 | 1 | |a Encyclopaedia of mathematical sciences / Invariant theory and algebraic transformation groups |v 8 | |
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Datensatz im Suchindex
| _version_ | 1805095956168835072 |
|---|---|
| adam_text |
IMAGE 1
CONTENTS
INTRODUCTION XV
NOTATION AND CONVENTIONS XVIII
1 ALGEBRAIC HOMOGENEOUS SPACES 1
1 HOMOGENEOUS SPACES 1
1.1 BASIC DEFINITIONS 1
1.2 TANGENT SPACES AND AUTOMORPHISMS 3
2 FIBRATIONS, BUNDLES, AND REPRESENTATIONS 3
2.1 HOMOGENEOUS BUNDLES 3
2.2 INDUCTION AND RESTRICTION 5
2.3 MULTIPLICITIES 6
2.4 REGULAR REPRESENTATION 6
2.5 HECKE ALGEBRAS 7
2.6 WEYL MODULES 8
3 CLASSES OF HOMOGENEOUS SPACES 10
3.1 REDUCTIONS 10
3.2 PROJECTIVE HOMOGENEOUS SPACES 11
3.3 AFFINE HOMOGENEOUS SPACES 11
3.4 QUASIAFFINE HOMOGENEOUS SPACES 13
2 COMPLEXITY AND RANK 15
4 LOCAL STRUCTURE THEOREMS 15
4.1 LOCALLY LINEARIZABLE ACTIONS 15
4.2 LOCAL STRUCTURE OF AN ACTION 16
4.3 LOCAL STRUCTURE THEOREM OF KNOP 19
5 COMPLEXITY AND RANK OF G-VARIETIES 20
5.1 BASIC DEFINITIONS 20
5.2 COMPLEXITY AND RANK OF SUBVARIETIES 20
5.3 WEIGHT SEMIGROUP 22
5.4 COMPLEXITY AND GROWTH OF MULTIPLICITIES 22
BIBLIOGRAFISCHE INFORMATIONEN HTTP://D-NB.INFO/1009117602
DIGITALISIERT DURCH
IMAGE 2
CONTENTS
6 COMPLEXITY AND MODALITY 24
6.1 MODALITY OF AN ACTION 24
6.2 COMPLEXITY AND 5-MODALITY 25
6.3 ADHERENCE OF 5-ORBITS 26
6.4 COMPLEXITY AND G-MODALITY 27
7 HOROSPHERICAL VARIETIES 28
7.1 HOROSPHERICAL SUBGROUPS AND VARIETIES 28
7.2 HOROSPHERICAL TYPE 30
7.3 HOROSPHERICAL CONTRACTION 30
8 GEOMETRY OF COTANGENT BUNDLES 31
8.1 SYMPLECTIC STRUCTURE 31
8.2 MOMENT MAP 31
8.3 LOCALIZATION 32
8.4 LOGARITHMIC VERSION 33
8.5 IMAGE OF THE MOMENT MAP 33
8.6 CORANK AND DEFECT 35
8.7 COTANGENT BUNDLE AND GEOMETRY OF AN ACTION 36
8.8 DOUBLED ACTIONS 37
9 COMPLEXITY AND RANK OF HOMOGENEOUS SPACES 39
9.1 GENERAL FORMULAE 39
9.2 REDUCTION TO REPRESENTATIONS 41
10 SPACES OF SMALL RANK AND COMPLEXITY 43
10.1 SPACES OF RANK 1 43
10.2 SPACES OF COMPLEXITY 1 44
11 DOUBLE CONES 46
11.1 HV-CONES AND DOUBLE CONES 47
11.2 COMPLEXITY AND RANK 49
11.3 FACTORIAL DOUBLE CONES OF COMPLEXITY 1 51
11.4 APPLICATIONS TO REPRESENTATION THEORY 52
11.5 SPHERICAL DOUBLE CONES 55
GENERAL THEORY OF EMBEDDINGS 57
12 THE LUNA-VUST THEORY 57
12.1 EQUIVARIANT CLASSIFICATION OF G-VARIETIES 57
12.2 UNIVERSAL MODEL 58
12.3 GERMS OF SUBVARIETIES 60
12.4 MORPHISMS, SEPARATION, AND PROPERNESS 61
13 SS-CHARTS 62
13.1 SS-CHARTS AND COLORED EQUIPMENT 62
13.2 COLORED DATA 63
13.3 LOCAL STRUCTURE 65
14 CLASSIFICATION OF G-MODELS 66
14.1 G-GERMS 66
14.2 G-MODELS 67
15 CASE OF COMPLEXITY 0 68
IMAGE 3
CONTENTS
15.1 COMBINATORIAL DESCRIPTION OF SPHERICAL VARIETIES 68 15.2
FUNCTORIALITY 70
15.3 ORBITS AND LOCAL GEOMETRY 71
16 CASE OF COMPLEXITY 1 72
16.1 GENERICALLY TRANSITIVE AND ONE-PARAMETRIC CASES 72 16.2 HYPERSPACE
73
16.3 HYPERCONES 75
16.4 COLORED DATA 77
16.5 EXAMPLES 80
16.6 LOCAL PROPERTIES 84
17 DIVISORS 84
17.1 REDUCTION TO B-STABLE DIVISORS 84
17.2 CARTIER DIVISORS 85
17.3 CASE OF COMPLEXITY 1 86
17.4 GLOBAL SECTIONS OF LINE BUNDLES 89
17.5 AMPLE DIVISORS 91
18 INTERSECTION THEORY 94
18.1 REDUCTION TO B-STABLE CYCLES 94
18.2 INTERSECTION OF DIVISORS 95
18.3 DIVISORS AND CURVES 99
18.4 CHOW RINGS 100
18.5 HALPHEN RING 101
18.6 GENERALIZATION OF THE BEZOUT THEOREM 102
INVARIANT VALUATIONS 105
19 G-VALUATIONS 106
19.1 BASIC PROPERTIES 106
19.2 CASE OF A REDUCTIVE GROUP 107
20 VALUATION CONES 108
20.1 HYPERSPACE 108
20.2 MAIN THEOREM 110
20.3 A GOOD G-MODEL 110
20.4 CRITERION OF GEOMETRICITY I LL
20.5 PROOF OF THE MAIN THEOREM 112
20.6 PARABOLIC INDUCTION 114
21 CENTRAL VALUATIONS 115
21.1 CENTRAL VALUATION CONE 115
21.2 CENTRAL AUTOMORPHISMS 116
21.3 VALUATIVE CHARACTERIZATION OF HOROSPHERICAL VARIETIES 118 21.4
G-VALUATIONS OF A CENTRAL DIVISOR 118
22 LITTLE WEYL GROUP 119
22.1 NORMALIZED MOMENT MAP 119
22.2 CONORMAL BUNDLE TO GENERAL [/-ORBITS 120
22.3 LITTLE WEYL GROUP 121
22.4 RELATION TO VALUATION CONES 123
IMAGE 4
CONTENTS
23 INVARIANT COLLECTIVE MOTION 124
23.1 POLARIZED COTANGENT BUNDLE 124
23.2 INTEGRATION OF INVARIANT COLLECTIVE MOTION 125
23.3 FLATS AND THEIR CLOSURES 126
23.4 NON-SYMPLECTICALLY STABLE CASE 128
23.5 PROOF OF THEOREM 22.13 129
23.6 SOURCES 130
23.7 ROOT SYSTEM OF A G-VARIETY 131
24 FORMAL CURVES 132
24.1 VALUATIONS VIA GERMS OF CURVES 132
24.2 VALUATIONS VIA FORMAL CURVES 133
SPHERICAL VARIETIES 135
25 VARIOUS CHARACTERIZATIONS OF SPHERICITY 136
25.1 SPHERICAL SPACES 136
25.2 "MULTIPLICITY-FREE" PROPERTY 137
25.3 WEAKLY SYMMETRIC SPACES AND GELFAND PAIRS 138 25.4 COMMUTATIVITY
139
25.5 GENERALIZATIONS 142
26 SYMMETRIC SPACES 145
26.1 ALGEBRAIC SYMMETRIC SPACES 145
26.2 0-STABLE TORI 146
26.3 MAXIMAL 0-FIXED TORI 147
26.4 MAXIMAL 0-SPLIT TORI 148
26.5 CLASSIFICATION 150
26.6 WEYL GROUP 154
26.7 SS-ORBITS 154
26.8 COLORED EQUIPMENT 155
26.9 COISOTROPY REPRESENTATION 157
26.10 FLATS 157
27 ALGEBRAIC MONOIDS AND GROUP EMBEDDINGS 158
27.1 ALGEBRAIC MONOIDS 158
27.2 REDUCTIVE MONOIDS 160
27.3 ORBITS 162
27.4 NORMALITY AND SMOOTHNESS 164
27.5 GROUP EMBEDDINGS 165
27.6 ENVELOPING AND ASYMPTOTIC SEMIGROUPS 168
28 S-VARIETIES 169
28.1 GENERAL S-VARIETIES 169
28.2 AFFINE CASE 170
28.3 SMOOTHNESS 173
29 TOROIDAL EMBEDDINGS 173
29.1 TOROIDAL VERSUS TORIC VARIETIES 174
29.2 SMOOTH TOROIDAL VARIETIES 174
29.3 COHOMOLOGY VANISHING 176
IMAGE 5
CONTENTS XIII
29.4 RIGIDITY 177
29.5 CHOW RINGS 178
29.6 CLOSURES OF FLATS 178
30 WONDERFUL VARIETIES 179
30.1 STANDARD COMPLETIONS 179
30.2 DEMAZURE EMBEDDING 181
30.3 CASE OF A SYMMETRIC SPACE 182
30.4 CANONICAL CLASS 183
30.5 COX RING 183
30.6 WONDERFUL VARIETIES 187
30.7 HOW TO CLASSIFY SPHERICAL SUBGROUPS 188
30.8 SPHERICAL SPACES OF RANK 1 189
30.9 LOCALIZATION OF WONDERFUL VARIETIES 191
30.10 TYPES OF SIMPLE ROOTS AND COLORS 193
30.11 COMBINATORIAL CLASSIFICATION OF SPHERICAL SUBGROUPS AND WONDERFUL
VARIETIES 194
30.12 PROOF OF THE CLASSIFICATION THEOREM 196
31 FROBENIUS SPLITTING 201
31.1 BASIC PROPERTIES 201
31.2 SPLITTING VIA DIFFERENTIAL FORMS 202
31.3 EXTENSION TO CHARACTERISTIC ZERO 204
31.4 SPHERICAL CASE 205
APPENDICES 207
A ALGEBRAIC GEOMETRY 207
A.I RATIONAL SINGULARITIES 207
A.2 MORI THEORY 208
A.3 SCHEMATIC POINTS 211
B GEOMETRIC VALUATIONS 212
C RATIONAL MODULES AND LINEARIZATION 214
D INVARIANT THEORY 216
E HILBERT SCHEMES 220
E.I CLASSICAL CASE 220
E.2 NESTED HILBERT SCHEME 222
E.3 INVARIANT HILBERT SCHEMES 223
REFERENCES 227
NAME INDEX 239
SUBJECT INDEX 243
NOTATION INDEX 249 |
| any_adam_object | 1 |
| author | Timašev, Dmitrij A. 1971- |
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| dewey-full | 516.35 |
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| dewey-ones | 516 - Geometry |
| dewey-raw | 516.35 |
| dewey-search | 516.35 |
| dewey-sort | 3516.35 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| edition | 1. ed. |
| format | Book |
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| id | DE-604.BV037388546 |
| illustrated | Illustrated |
| indexdate | 2024-07-20T11:07:31Z |
| institution | BVB |
| isbn | 3642183980 9783642183980 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-022541491 |
| oclc_num | 729920668 |
| open_access_boolean | |
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| owner_facet | DE-19 DE-BY-UBM DE-188 DE-29T |
| physical | XXI, 253 S. graph. Darst. |
| publishDate | 2011 |
| publishDateSearch | 2011 |
| publishDateSort | 2011 |
| publisher | Springer |
| record_format | marc |
| series | Encyclopaedia of Mathematical Sciences |
| series2 | Encyclopaedia of Mathematical Sciences Encyclopaedia of mathematical sciences / Invariant theory and algebraic transformation groups |
| spelling | Timašev, Dmitrij A. 1971- Verfasser (DE-588)1012190994 aut Homogeneous spaces and equivariant embeddings Dmitry A. Timashev 1. ed. Berlin [u.a.] Springer 2011 XXI, 253 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Encyclopaedia of Mathematical Sciences 138 Encyclopaedia of mathematical sciences / Invariant theory and algebraic transformation groups 8 Homogener Raum (DE-588)4025787-3 gnd rswk-swf Äquivariante Einbettung (DE-588)4207959-7 gnd rswk-swf Algebraische Gruppe (DE-588)4001164-1 gnd rswk-swf Algebraische Gruppe (DE-588)4001164-1 s Äquivariante Einbettung (DE-588)4207959-7 s Homogener Raum (DE-588)4025787-3 s DE-604 Erscheint auch als Online-Ausgabe 978-3-642-18399-7 Invariant theory and algebraic transformation groups Encyclopaedia of mathematical sciences 8 (DE-604)BV014336202 8 Encyclopaedia of Mathematical Sciences 138 (DE-604)BV024126459 138 X:MVB text/html http://deposit.dnb.de/cgi-bin/dokserv?id=3639504&prov=M&dok_var=1&dok_ext=htm Inhaltstext DNB Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=022541491&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Timašev, Dmitrij A. 1971- Homogeneous spaces and equivariant embeddings Encyclopaedia of Mathematical Sciences Homogener Raum (DE-588)4025787-3 gnd Äquivariante Einbettung (DE-588)4207959-7 gnd Algebraische Gruppe (DE-588)4001164-1 gnd |
| subject_GND | (DE-588)4025787-3 (DE-588)4207959-7 (DE-588)4001164-1 |
| title | Homogeneous spaces and equivariant embeddings |
| title_auth | Homogeneous spaces and equivariant embeddings |
| title_exact_search | Homogeneous spaces and equivariant embeddings |
| title_full | Homogeneous spaces and equivariant embeddings Dmitry A. Timashev |
| title_fullStr | Homogeneous spaces and equivariant embeddings Dmitry A. Timashev |
| title_full_unstemmed | Homogeneous spaces and equivariant embeddings Dmitry A. Timashev |
| title_short | Homogeneous spaces and equivariant embeddings |
| title_sort | homogeneous spaces and equivariant embeddings |
| topic | Homogener Raum (DE-588)4025787-3 gnd Äquivariante Einbettung (DE-588)4207959-7 gnd Algebraische Gruppe (DE-588)4001164-1 gnd |
| topic_facet | Homogener Raum Äquivariante Einbettung Algebraische Gruppe |
| url | http://deposit.dnb.de/cgi-bin/dokserv?id=3639504&prov=M&dok_var=1&dok_ext=htm http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=022541491&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV014336202 (DE-604)BV024126459 |
| work_keys_str_mv | AT timasevdmitrija homogeneousspacesandequivariantembeddings |