Geometric invariant theory:
Saved in:
| Main Authors: | , , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Berlin [u.a.]
Springer
2002
|
| Edition: | Third enlarged edition, Third reprint |
| Series: | Ergebnisse der Mathematik und ihrer Grenzgebiete
Neue Folge ; 34 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XIV, 292 Seiten |
| ISBN: | 9783642634000 |
Staff View
MARC
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| 245 | 1 | 0 | |a Geometric invariant theory |c D. Mumford ; J. Fogarty ; F. Kirwan |
| 250 | |a Third enlarged edition, Third reprint | ||
| 264 | 1 | |a Berlin [u.a.] |b Springer |c 2002 | |
| 264 | 4 | |c © 1994 | |
| 300 | |a XIV, 292 Seiten | ||
| 336 | |b txt |2 rdacontent | ||
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| 700 | 1 | |a Kirwan, Frances |d 1959- |e Verfasser |0 (DE-588)172187338 |4 aut | |
| 775 | 0 | 8 | |i Nachdruck von |a Mumford, David |t Geometric invariant theory |d Springer, 1994 |z 3-540-56963-4 |
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Record in the Search Index
| _version_ | 1804131846392381440 |
|---|---|
| adam_text | Contents
Chapter
0.
Preliminaries
...................................... 1
1.
Definitions
........................................... 2
2.
First properties
...................................... 4
3.
Good and bad actions
................................ 9
4.
Farther properties
.................................... 13
5.
Resumé
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
covariante
—
S^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
hyperkähler
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
S
........................................ 202
Appendix to Chapter
3 ........................................ 205
Appendix to Chapter
Ą
........................................ 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 | BV019267533 |
| classification_rvk | SK 240 |
| ctrlnum | (OCoLC)180017115 (DE-599)BVBBV019267533 |
| discipline | Mathematik |
| edition | Third enlarged edition, Third reprint |
| format | Book |
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| id | DE-604.BV019267533 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-09T19:43:25Z |
| institution | BVB |
| isbn | 9783642634000 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-012031312 |
| oclc_num | 180017115 |
| open_access_boolean | |
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| owner_facet | DE-703 DE-384 DE-19 DE-BY-UBM DE-355 DE-BY-UBR DE-20 DE-11 |
| physical | XIV, 292 Seiten |
| publishDate | 2002 |
| publishDateSearch | 2002 |
| publishDateSort | 2002 |
| publisher | Springer |
| record_format | marc |
| series | Ergebnisse der Mathematik und ihrer Grenzgebiete |
| 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, Third reprint Berlin [u.a.] Springer 2002 © 1994 XIV, 292 Seiten txt rdacontent n rdamedia nc rdacarrier Ergebnisse der Mathematik und ihrer Grenzgebiete : Neue Folge 34 1994 Algebraische Geometrie (DE-588)4001161-6 gnd rswk-swf Invariantentheorie (DE-588)4162209-1 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 Fogarty, John 1934- Verfasser (DE-588)1056024534 aut Kirwan, Frances 1959- Verfasser (DE-588)172187338 aut Nachdruck von Mumford, David Geometric invariant theory Springer, 1994 3-540-56963-4 Erscheint auch als Online-Ausgabe 978-3-642-57916-5 Ergebnisse der Mathematik und ihrer Grenzgebiete Neue Folge ; 34 (DE-604)BV005871160 34 Digitalisierung UB Regensburg application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=012031312&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 Ergebnisse der Mathematik und ihrer Grenzgebiete Algebraische Geometrie (DE-588)4001161-6 gnd Invariantentheorie (DE-588)4162209-1 gnd Geometrische Invariantentheorie (DE-588)4156712-2 gnd |
| subject_GND | (DE-588)4001161-6 (DE-588)4162209-1 (DE-588)4156712-2 |
| 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 | Algebraische Geometrie (DE-588)4001161-6 gnd Invariantentheorie (DE-588)4162209-1 gnd Geometrische Invariantentheorie (DE-588)4156712-2 gnd |
| topic_facet | Algebraische Geometrie Invariantentheorie Geometrische Invariantentheorie |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=012031312&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 |