Geometric invariant theory:
Saved in:
| Main Authors: | , , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Berlin ; Heidelberg
Springer
1994
|
| Edition: | Third enlarged edition |
| Series: | Ergebnisse der Mathematik und ihrer Grenzgebiete / Neue Folge
34 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XIV, 292 Seiten Illustrationen |
| ISBN: | 3540569634 0387569634 |
Staff View
MARC
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| 100 | 1 | |a Mumford, David |d 1937- |e Verfasser |0 (DE-588)115549021 |4 aut | |
| 245 | 1 | 0 | |a Geometric invariant theory |c D. Mumford ; J. Fogarty ; F. Kirwan |
| 250 | |a Third enlarged edition | ||
| 264 | 1 | |a Berlin ; Heidelberg |b Springer |c 1994 | |
| 264 | 4 | |c © 1994 | |
| 300 | |a XIV, 292 Seiten |b Illustrationen | ||
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| 490 | 1 | |a Ergebnisse der Mathematik und ihrer Grenzgebiete / Neue Folge |v 34 | |
| 650 | 4 | |a Geometria algebraica | |
| 650 | 4 | |a Invariantes | |
| 650 | 4 | |a Teoría de módulos | |
| 650 | 0 | 7 | |a Geometrische Invariantentheorie |0 (DE-588)4156712-2 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Invariantentheorie |0 (DE-588)4162209-1 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Algebraische Geometrie |0 (DE-588)4001161-6 |2 gnd |9 rswk-swf |
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Record in the Search Index
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| adam_text | Contents
Chapter 0. Preliminaries 1
1. Definitions 2
2. First properties 4
3. Good and bad actions 9
4. Further properties 13
5. Resume of some results of Grothendieck 19
Chapter 1. Fundamental theorems for the actions
of reductive groups 24
1. Definitions 24
2. The affine case 27
3. Linearization of an invertible sheaf 30
4. The general case 36
5. Functional properties 44
Chapter 2. Analysis of stability 48
1. A numeral criterion 48
2. The flag complex 55
3. Applications 63
Chapter 3. An elementary example 67
1. Pre stability 67
2. Stability 72
Chapter 4 Further examples 76
1. Binary quantics 76
2. Hypersurfaces 79
3. Counter examples 83
4. Sequences of linear subspaces 86
5. The projective adjoint action 88
6. Space curves 89
XIV Contents
Chapter 5. The problem of moduli — 1st construction 96
1. General discussion 96
2. Moduli as an orbit space 98
3. First chern classes 104
4. Utilization of 4.6 109
Chapter 6. Abelian schemes 115
1. Duals 115
2. Polarizations 120
3. Deformations 124
Chapter 7. The method of covariants — ^ d construction 127
1. The technique 127
2. Moduli as an orbit space 129
3. The covariant 138
4. Application to curves 142
Chapter 8. The moment map 144
1. Symplectic geometry 144
2. Symplectic quotients and geometric invariant theory .. 148
3. Kahler and hyperkahler quotients 152
4. Singular quotients 156
5. Geometry of the moment map 160
6. The cohomology of quotients: the symplectic case 164
7. The cohomology of quotients: the algebraic case 172
8. Vector bundles and the Yang Mills functional 181
9. Yang Mills theory over Riemann surfaces 185
Appendix to Chapter 1 191
Appendix to Chapter 2 202
Appendix to Chapter 3 205
Appendix to Chapter 4 206
Appendix to Chapter 5 217
Appendix to Chapter 7 234
References 253
Index of definitions and notations 291
|
| any_adam_object | 1 |
| author | Mumford, David 1937- Fogarty, John 1934- Kirwan, Frances 1959- |
| author_GND | (DE-588)115549021 (DE-588)1056024534 (DE-588)172187338 |
| author_facet | Mumford, David 1937- Fogarty, John 1934- Kirwan, Frances 1959- |
| author_role | aut aut aut |
| author_sort | Mumford, David 1937- |
| author_variant | d m dm j f jf f k fk |
| building | Verbundindex |
| bvnumber | BV009559101 |
| classification_rvk | SK 240 |
| classification_tum | MAT 149f |
| ctrlnum | (OCoLC)318279180 (DE-599)BVBBV009559101 |
| dewey-full | 516.35 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 516 - Geometry |
| dewey-raw | 516.35 |
| dewey-search | 516.35 |
| dewey-sort | 3516.35 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| edition | Third enlarged edition |
| format | Book |
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| id | DE-604.BV009559101 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T17:37:07Z |
| institution | BVB |
| isbn | 3540569634 0387569634 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-006316310 |
| oclc_num | 318279180 |
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| physical | XIV, 292 Seiten Illustrationen |
| publishDate | 1994 |
| publishDateSearch | 1994 |
| publishDateSort | 1994 |
| publisher | Springer |
| record_format | marc |
| series2 | Ergebnisse der Mathematik und ihrer Grenzgebiete / Neue Folge |
| spelling | Mumford, David 1937- Verfasser (DE-588)115549021 aut Geometric invariant theory D. Mumford ; J. Fogarty ; F. Kirwan Third enlarged edition Berlin ; Heidelberg Springer 1994 © 1994 XIV, 292 Seiten Illustrationen txt rdacontent n rdamedia nc rdacarrier Ergebnisse der Mathematik und ihrer Grenzgebiete / Neue Folge 34 Geometria algebraica Invariantes Teoría de módulos Geometrische Invariantentheorie (DE-588)4156712-2 gnd rswk-swf Invariantentheorie (DE-588)4162209-1 gnd rswk-swf Algebraische Geometrie (DE-588)4001161-6 gnd rswk-swf Geometrische Invariantentheorie (DE-588)4156712-2 s DE-604 Invariantentheorie (DE-588)4162209-1 s Algebraische Geometrie (DE-588)4001161-6 s Fogarty, John 1934- Verfasser (DE-588)1056024534 aut Kirwan, Frances 1959- Verfasser (DE-588)172187338 aut Neue Folge Ergebnisse der Mathematik und ihrer Grenzgebiete 34 (DE-604)BV005871160 34 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=006316310&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Mumford, David 1937- Fogarty, John 1934- Kirwan, Frances 1959- Geometric invariant theory Geometria algebraica Invariantes Teoría de módulos Geometrische Invariantentheorie (DE-588)4156712-2 gnd Invariantentheorie (DE-588)4162209-1 gnd Algebraische Geometrie (DE-588)4001161-6 gnd |
| subject_GND | (DE-588)4156712-2 (DE-588)4162209-1 (DE-588)4001161-6 |
| title | Geometric invariant theory |
| title_auth | Geometric invariant theory |
| title_exact_search | Geometric invariant theory |
| title_full | Geometric invariant theory D. Mumford ; J. Fogarty ; F. Kirwan |
| title_fullStr | Geometric invariant theory D. Mumford ; J. Fogarty ; F. Kirwan |
| title_full_unstemmed | Geometric invariant theory D. Mumford ; J. Fogarty ; F. Kirwan |
| title_short | Geometric invariant theory |
| title_sort | geometric invariant theory |
| topic | Geometria algebraica Invariantes Teoría de módulos Geometrische Invariantentheorie (DE-588)4156712-2 gnd Invariantentheorie (DE-588)4162209-1 gnd Algebraische Geometrie (DE-588)4001161-6 gnd |
| topic_facet | Geometria algebraica Invariantes Teoría de módulos Geometrische Invariantentheorie Invariantentheorie Algebraische Geometrie |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=006316310&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV005871160 |
| work_keys_str_mv | AT mumforddavid geometricinvarianttheory AT fogartyjohn geometricinvarianttheory AT kirwanfrances geometricinvarianttheory |