Geometric Invariant Theory: 34 - Rilegato

Mumford, David; Fogarty, John; Kirwan, Frances

 
9783540569633: Geometric Invariant Theory: 34
Rilegato
ISBN 10: 3540569634 ISBN 13: 9783540569633
Casa editrice: Springer Nature, 2002

Sinossi

<p>This standard reference on applications of invariant theory to the construction of moduli spaces is a systematic exposition of the geometric aspects of classical theory of polynomial invariants. This new, revised edition is completely updated and enlarged with an additional chapter on the moment map by Professor Frances Kirwan. It includes a fully updated bibliography of work in this area.</p>

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Contenuti

0. Preliminaries.- 1. Definitions.- 2. First properties.- 3. Good and bad actions.- 4. Further properties.- 5. Resumé of some results of Grothendieck.- 1. Fundamental theorems for the actions of reductive groups.- 1. Definitions.- 2. The affine case.- 3. Linearization of an invertible sheaf.- 4. The general case.- 5. Functional properties.- 2. Analysis of stability.- 1. A numeral criterion.- 2. The flag complex.- 3. Applications.- 3. An elementary example.- 1. Pre-stability.- 2. Stability.- 4. Further examples.- 1. Binary quantics.- 2. Hypersurfaces.- 3. Counter-examples.- 4. Sequences of linear subspaces.- 5. The projective adjoint action.- 6. Space curves.- 5. The problem of moduli — 1st construction.- 1. General discussion.- 2. Moduli as an orbit space.- 3. First chern classes.- 4. Utilization of 4.6.- 6. Abelian schemes.- 1. Duals.- 2. Polarizations.- 3. Deformations.- 7. The method of covariants — 2nd construction.- 1. The technique.- 2. Moduli as an orbit space.- 3. The covariant.- 4. Application to curves.- 8. The moment map.- 1. Symplectic geometry.- 2. Symplectic quotients and geometric invariant theory.- 3. Kähler and hyperkähler quotients.- 4. Singular quotients.- 5. Geometry of the moment map.- 6. The cohomology of quotients: the symplectic case.- 7. The cohomology of quotients: the algebraic case.- 8. Vector bundles and the Yang-Mills functional.- 9. Yang-Mills theory over Riemann surfaces.- Appendix to Chapter 1.- Appendix to Chapter 2.- Appendix to Chapter 3.- Appendix to Chapter 4.- Appendix to Chapter 5.- Appendix to Chapter 7.- References.- Index of definitions and notations.

Product Description

Book by Mumford David Fogarty John Kirwan Frances

Le informazioni nella sezione "Su questo libro" possono far riferimento a edizioni diverse di questo titolo.

Editore
Springer Nature
Data di pubblicazione
2002
Lingua
Inglese
ISBN 10 
3540569634
ISBN 13 
9783540569633
Rilegatura
Copertina rigida
Numero edizione
3
Numero di pagine
308
Contatto del produttore
non disponibile
Persona responsabile
Springer Nature Customer Service Center GmbH
ProductSafety@springernature.com

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Heidelberg
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Germania

Altre edizioni note dello stesso titolo

9783642634000: Geometric Invariant Theory: 34

Edizione in evidenza

ISBN 10:  3642634001 ISBN 13:  9783642634000
Casa editrice: Springer, 2012
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