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Geometric Invariant Theory

BuchKartoniert, Paperback
294 Seiten
Englisch
Springererschienen am29.10.20123. Aufl.
Geometric Invariant Theory by Mumford/Fogarty (the first edition was published in 1965, a second, enlarged edition appeared in 1982) is the standard reference on applications of invariant theory to the construction of moduli spaces.mehr
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BuchGebunden
EUR160,45
BuchKartoniert, Paperback
EUR160,45

Produkt

KlappentextGeometric Invariant Theory by Mumford/Fogarty (the first edition was published in 1965, a second, enlarged edition appeared in 1982) is the standard reference on applications of invariant theory to the construction of moduli spaces.
Details
ISBN/GTIN978-3-642-63400-0
ProduktartBuch
EinbandartKartoniert, Paperback
Verlag
Erscheinungsjahr2012
Erscheinungsdatum29.10.2012
Auflage3. Aufl.
ReiheErgebnisse der Mathematik und ihrer Grenzgebiete. 2. Folge
Seiten294 Seiten
SpracheEnglisch
Gewicht480 g
IllustrationenXIV, 294 p.
Artikel-Nr.15399405

Inhalt/Kritik

Inhaltsverzeichnis
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.mehr

Autor

David Mumford was born on June 11, 1937 in England and has been associated with Harvard University continuously from entering as freshman to his present position of Higgins Professor of Mathematics.
Mumford worked in the fields of Algebraic Gemetry in the 60's and 70's, concentrating especially on the theory of moduli spaces: spaces which classify all objects of some type, such as all curves of a given genus or all vector bundles on a fixed curve of given rank and degree. Mumford was awarded the Fields Medal in 1974 for his work on moduli spaces and algebraic surfaces. He is presently working on the mathematics of pattern recognition and artificial intelligence.