Groups, generators, syzygies, and orbits in invariant theory
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| Format: | Buch |
| Sprache: | English Russian |
| Veröffentlicht: |
Providence, R.I.
American Mathematical Society
1992
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| Schriftenreihe: | Translations of mathematical monographs
100 |
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| Online-Zugang: | Inhaltsverzeichnis |
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| 100 | 1 | |a Popov, Vladimir L. |e Verfasser |4 aut | |
| 240 | 1 | 0 | |a Gruppy, obrazujuščie, sizigii i orbity v teorii invariantov |
| 245 | 1 | 0 | |a Groups, generators, syzygies, and orbits in invariant theory |c V. L. Popov |
| 264 | 1 | |a Providence, R.I. |b American Mathematical Society |c 1992 | |
| 300 | |a VI, 245 S. |b graph. Darst. | ||
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| 490 | 1 | |a Translations of mathematical monographs |v 100 | |
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Datensatz im Suchindex
| _version_ | 1819576762020921344 |
|---|---|
| adam_text | Contents
Introduction 1
Notation and Terminology 19
CHAPTER 1. The Role of Reductive Groups in Invariant Theory 23
§1. Reductive groups and the generalized Hilbert s 14th problem 23
§2. Quasihomogeneous varieties of reductive groups and the
original Hilbert s 14th problem 25
CHAPTER 2. Constructive Invariant Theory 29
§1. Formulation and reduction of the problem 29
§2. A bound on the degree of a system of parameters and the
main theorem 33
§3. The radical of the ideal / and the approach suggested by
Dieudonne and Carrell 40
CHAPTER 3. The Degree of the Poincare Series of the Algebra of
Invariants and a Finiteness Theorem for
Representations wit Free Algebra of Invariants 43
§ 1. The degree of the Poincare series and a functional equation 43
§2. The zonohedron of weights 51
§3. Finiteness theorems 56
CHAPTER 4. Syzygies in Invariant Theory 61
§0. A description of the results and additional notation 61
§ 1. Monotonicity theorems 64
§2. Bounds on hdk[V]G for certain types of groups 68
§3. Estimating hdk[V]G with the aid of one dimensional tori of
G 76
§4. Majorizing theorems for multiplicities, generic stabilizers,
and stability 82
§5. Torus T for the classical simple groups of rank 2 87
§6. Torus T for the exceptional simple groups 94
§7. Proof of the main theorem: the first case 100
§8. Proof of the main theorem: the second case 104
V
vi CONTENTS
§9. Proof of the main theorem: the third case 113
§10. Examples 119
CHAPTER 5. Representations with Free Modules of Co variants 127
§1. Connections with equidimensionality: finiteness theorems 127
§2. Classification and equivalent characterizations: Igusa s
condition 135
CHAPTER 6. A Classification of Normal Affine Quasihomogeneous
Varieties of SL2 147
§1. Some general results and the beginning of classification 147
§2. The conclusion of classification 154
§3. Application: the structure of orbit closures in
finite dimensional rational SL2 modules 164
CHAPTER 7. Quasihomogeneous Curves, Surfaces, and Solids 167
§1. A classification of irreducible quasihomogeneous curves 167
§2. A classification of irreducible affine surfaces with algebraic
groups of automorphisms acting transitively on the
complement of a finite number of points 176
§3. A classification of irreducible affine solids with algebraic
groups of automorphisms acting transitively on the
complement of a finite number of points 181
Appendix 201
§1. Appendix to Chapter 1 201
§2. Appendix to Chapter 2 203
§3. Appendix to Chapter 3 204
§4. Appendix to Chapter 4 213
§5. Appendix to Chapter 5 216
§6. Appendix to Chapter 6 225
Bibliography 231
Subject Index 243
|
| any_adam_object | 1 |
| author | Popov, Vladimir L. |
| author_facet | Popov, Vladimir L. |
| author_role | aut |
| author_sort | Popov, Vladimir L. |
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| building | Verbundindex |
| bvnumber | BV005594008 |
| callnumber-first | Q - Science |
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| callnumber-sort | QA 3201 |
| callnumber-subject | QA - Mathematics |
| classification_rvk | SK 240 SK 260 |
| classification_tum | MAT 200f MAT 202f |
| ctrlnum | (OCoLC)25628966 (DE-599)BVBBV005594008 |
| dewey-full | 512/.944 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 512 - Algebra |
| dewey-raw | 512/.944 |
| dewey-search | 512/.944 |
| dewey-sort | 3512 3944 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| format | Book |
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| id | DE-604.BV005594008 |
| illustrated | Illustrated |
| indexdate | 2024-12-23T11:40:31Z |
| institution | BVB |
| isbn | 0821845578 9780821853351 |
| language | English Russian |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-003503967 |
| oclc_num | 25628966 |
| open_access_boolean | |
| owner | DE-384 DE-12 DE-355 DE-BY-UBR DE-703 DE-19 DE-BY-UBM DE-634 DE-188 DE-91G DE-BY-TUM |
| owner_facet | DE-384 DE-12 DE-355 DE-BY-UBR DE-703 DE-19 DE-BY-UBM DE-634 DE-188 DE-91G DE-BY-TUM |
| physical | VI, 245 S. graph. Darst. |
| publishDate | 1992 |
| publishDateSearch | 1992 |
| publishDateSort | 1992 |
| publisher | American Mathematical Society |
| record_format | marc |
| series | Translations of mathematical monographs |
| series2 | Translations of mathematical monographs |
| spellingShingle | Popov, Vladimir L. Groups, generators, syzygies, and orbits in invariant theory Translations of mathematical monographs Invariants Invariants ram Algebraische Geometrie (DE-588)4001161-6 gnd Algebraische Mannigfaltigkeit (DE-588)4128509-8 gnd Invariante (DE-588)4128781-2 gnd Invariantentheorie (DE-588)4162209-1 gnd Reduktive Gruppe (DE-588)4177313-5 gnd |
| subject_GND | (DE-588)4001161-6 (DE-588)4128509-8 (DE-588)4128781-2 (DE-588)4162209-1 (DE-588)4177313-5 |
| title | Groups, generators, syzygies, and orbits in invariant theory |
| title_alt | Gruppy, obrazujuščie, sizigii i orbity v teorii invariantov |
| title_auth | Groups, generators, syzygies, and orbits in invariant theory |
| title_exact_search | Groups, generators, syzygies, and orbits in invariant theory |
| title_full | Groups, generators, syzygies, and orbits in invariant theory V. L. Popov |
| title_fullStr | Groups, generators, syzygies, and orbits in invariant theory V. L. Popov |
| title_full_unstemmed | Groups, generators, syzygies, and orbits in invariant theory V. L. Popov |
| title_short | Groups, generators, syzygies, and orbits in invariant theory |
| title_sort | groups generators syzygies and orbits in invariant theory |
| topic | Invariants Invariants ram Algebraische Geometrie (DE-588)4001161-6 gnd Algebraische Mannigfaltigkeit (DE-588)4128509-8 gnd Invariante (DE-588)4128781-2 gnd Invariantentheorie (DE-588)4162209-1 gnd Reduktive Gruppe (DE-588)4177313-5 gnd |
| topic_facet | Invariants Algebraische Geometrie Algebraische Mannigfaltigkeit Invariante Invariantentheorie Reduktive Gruppe |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=003503967&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV000002394 |
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