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Geometric Invariant Theory Softcover reprint of the original 3rd ed. 1994 [Mīkstie vāki]

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  • Formāts: Paperback / softback, 294 pages, height x width: 235x155 mm, weight: 480 g, XIV, 294 p., 1 Paperback / softback
  • Sērija : Ergebnisse der Mathematik und ihrer Grenzgebiete. 2. Folge 34
  • Izdošanas datums: 29-Oct-2012
  • Izdevniecība: Springer-Verlag Berlin and Heidelberg GmbH & Co. K
  • ISBN-10: 3642634001
  • ISBN-13: 9783642634000
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Geometric Invariant Theory Softcover reprint of the original 3rd ed. 1994Palielināt
  • Formāts: Paperback / softback, 294 pages, height x width: 235x155 mm, weight: 480 g, XIV, 294 p., 1 Paperback / softback
  • Sērija : Ergebnisse der Mathematik und ihrer Grenzgebiete. 2. Folge 34
  • Izdošanas datums: 29-Oct-2012
  • Izdevniecība: Springer-Verlag Berlin and Heidelberg GmbH & Co. K
  • ISBN-10: 3642634001
  • ISBN-13: 9783642634000
Citas grāmatas par šo tēmu:
Permanent link: https://www.kriso.lv/db/9783642634000.html
Keywords:
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. This third, revised edition has been long awaited for by the mathematical community. It is now appearing in a completely updated and enlarged version with an additional chapter on the moment map by Prof. Frances Kirwan (Oxford) and a fully updated bibliography of work in this area. The book deals firstly with actions of algebraic groups on algebraic varieties, separating orbits by invariants and construction quotient spaces; and secondly with applications of this theory to the construction of moduli spaces. It is a systematic exposition of the geometric aspects of the classical theory of polynomial invariants.

Papildus informācija

Springer Book Archives
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.