Geometric invariant theory:
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Berlin [u.a.]
Springer
1982
|
| Edition: | 2., enl. ed. |
| Series: | Ergebnisse der Mathematik und ihrer Grenzgebiete
34 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | 219 S. |
| ISBN: | 3540112901 0387112901 |
Staff View
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| 245 | 1 | 0 | |a Geometric invariant theory |c D. Mumford ; J. Fogarty |
| 250 | |a 2., enl. ed. | ||
| 264 | 1 | |a Berlin [u.a.] |b Springer |c 1982 | |
| 300 | |a 219 S. | ||
| 336 | |b txt |2 rdacontent | ||
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| 490 | 1 | |a Ergebnisse der Mathematik und ihrer Grenzgebiete |v 34 | |
| 650 | 4 | |a Géométrie algébrique | |
| 650 | 7 | |a Géométrie algébrique |2 ram | |
| 650 | 7 | |a Invarianten |2 gtt | |
| 650 | 4 | |a Invariants | |
| 650 | 7 | |a Invariants |2 ram | |
| 650 | 4 | |a Modules, Théorie des | |
| 650 | 7 | |a Modules, théorie des |2 ram | |
| 650 | 7 | |a géométrie algébrique |2 inriac | |
| 650 | 7 | |a invariant |2 inriac | |
| 650 | 7 | |a stabilité |2 inriac | |
| 650 | 7 | |a théorie module |2 inriac | |
| 650 | 4 | |a Geometry, Algebraic | |
| 650 | 4 | |a Invariants | |
| 650 | 4 | |a Moduli theory | |
| 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 |
| 650 | 0 | 7 | |a Geometrische Invariantentheorie |0 (DE-588)4156712-2 |2 gnd |9 rswk-swf |
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Record in the Search Index
| _version_ | 1804136091023835136 |
|---|---|
| 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 numerical criterion 48
2. The flag complex 55
3. Applications 03
Chapter 3. An elementary example 67
1. Pre stability 67
2. Stability 72
Chapter 4. Further examples 74
1. Binary quantics 70
2. Hypersurfaces 79
3. Counter examples 83
4. Sequences of linear subspaces 86
5. The projective adjoint action 88
6. Space curves 89
Chapter 5. The problem of moduli — 1* construction 90
1. General discussion 90
2. Moduli as an orbit space 98
3. First chern classes 104
4. Utilization of 4.0 109
XII Contents
Chapter 6. Abelian schemes 115
1. Duals 115
2. Polarizations 120
3. Deformations 124
Chapter 7. The method of covariants — 2nd construction 127
1. The technique 127
2. Moduli as an orbit space 129
3. Thecovariant 138
4. Application to curves 142
Appendix to Chapter 1 145
Appendix to Chapter 2 156
Appendix to Chapter 3 159
Appendix to Chapter 4 160
Appendix to Chapter 5 171
Appendix to Chapter 7 188
References 206
Index of definitions 221
|
| adam_txt |
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 numerical criterion 48
2. The flag complex 55
3. Applications 03
Chapter 3. An elementary example 67
1. Pre stability 67
2. Stability 72
Chapter 4. Further examples 74
1. Binary quantics 70
2. Hypersurfaces 79
3. Counter examples 83
4. Sequences of linear subspaces 86
5. The projective adjoint action 88
6. Space curves 89
Chapter 5. The problem of moduli — 1* construction 90
1. General discussion 90
2. Moduli as an orbit space 98
3. First chern classes 104
4. Utilization of 4.0 109
XII Contents
Chapter 6. Abelian schemes 115
1. Duals 115
2. Polarizations 120
3. Deformations 124
Chapter 7. The method of covariants — 2nd construction 127
1. The technique 127
2. Moduli as an orbit space 129
3. Thecovariant 138
4. Application to curves 142
Appendix to Chapter 1 145
Appendix to Chapter 2 156
Appendix to Chapter 3 159
Appendix to Chapter 4 160
Appendix to Chapter 5 171
Appendix to Chapter 7 188
References 206
Index of definitions 221 |
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| author | Mumford, David 1937- Fogarty, John |
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| author_facet | Mumford, David 1937- Fogarty, John |
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| callnumber-subject | QA - Mathematics |
| classification_rvk | SK 240 |
| ctrlnum | (OCoLC)8034629 (DE-599)BVBBV022117196 |
| dewey-full | 516.3/5 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 516 - Geometry |
| dewey-raw | 516.3/5 |
| dewey-search | 516.3/5 |
| dewey-sort | 3516.3 15 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| discipline_str_mv | Mathematik |
| edition | 2., enl. ed. |
| format | Book |
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| id | DE-604.BV022117196 |
| illustrated | Not Illustrated |
| index_date | 2024-07-02T16:16:02Z |
| indexdate | 2024-07-09T20:50:53Z |
| institution | BVB |
| isbn | 3540112901 0387112901 |
| language | English |
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| oclc_num | 8034629 |
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| owner_facet | DE-706 |
| physical | 219 S. |
| publishDate | 1982 |
| publishDateSearch | 1982 |
| publishDateSort | 1982 |
| publisher | Springer |
| record_format | marc |
| series | Ergebnisse der Mathematik und ihrer Grenzgebiete |
| series2 | Ergebnisse der Mathematik und ihrer Grenzgebiete |
| spelling | Mumford, David 1937- Verfasser (DE-588)115549021 aut Geometric invariant theory D. Mumford ; J. Fogarty 2., enl. ed. Berlin [u.a.] Springer 1982 219 S. txt rdacontent n rdamedia nc rdacarrier Ergebnisse der Mathematik und ihrer Grenzgebiete 34 Géométrie algébrique Géométrie algébrique ram Invarianten gtt Invariants Invariants ram Modules, Théorie des Modules, théorie des ram géométrie algébrique inriac invariant inriac stabilité inriac théorie module inriac Geometry, Algebraic Moduli theory Invariantentheorie (DE-588)4162209-1 gnd rswk-swf Algebraische Geometrie (DE-588)4001161-6 gnd rswk-swf Geometrische Invariantentheorie (DE-588)4156712-2 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 1\p DE-604 Fogarty, John Verfasser aut Ergebnisse der Mathematik und ihrer Grenzgebiete 34 (DE-604)BV005871160 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=015332060&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Mumford, David 1937- Fogarty, John Geometric invariant theory Ergebnisse der Mathematik und ihrer Grenzgebiete Géométrie algébrique Géométrie algébrique ram Invarianten gtt Invariants Invariants ram Modules, Théorie des Modules, théorie des ram géométrie algébrique inriac invariant inriac stabilité inriac théorie module inriac Geometry, Algebraic Moduli theory Invariantentheorie (DE-588)4162209-1 gnd Algebraische Geometrie (DE-588)4001161-6 gnd Geometrische Invariantentheorie (DE-588)4156712-2 gnd |
| subject_GND | (DE-588)4162209-1 (DE-588)4001161-6 (DE-588)4156712-2 |
| title | Geometric invariant theory |
| title_auth | Geometric invariant theory |
| title_exact_search | Geometric invariant theory |
| title_exact_search_txtP | Geometric invariant theory |
| title_full | Geometric invariant theory D. Mumford ; J. Fogarty |
| title_fullStr | Geometric invariant theory D. Mumford ; J. Fogarty |
| title_full_unstemmed | Geometric invariant theory D. Mumford ; J. Fogarty |
| title_short | Geometric invariant theory |
| title_sort | geometric invariant theory |
| topic | Géométrie algébrique Géométrie algébrique ram Invarianten gtt Invariants Invariants ram Modules, Théorie des Modules, théorie des ram géométrie algébrique inriac invariant inriac stabilité inriac théorie module inriac Geometry, Algebraic Moduli theory Invariantentheorie (DE-588)4162209-1 gnd Algebraische Geometrie (DE-588)4001161-6 gnd Geometrische Invariantentheorie (DE-588)4156712-2 gnd |
| topic_facet | Géométrie algébrique Invarianten Invariants Modules, Théorie des Modules, théorie des géométrie algébrique invariant stabilité théorie module Geometry, Algebraic Moduli theory Invariantentheorie Algebraische Geometrie Geometrische Invariantentheorie |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=015332060&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 |