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[美] 芒福德(Mumford D.) 著
出版社: 世界图书出版公司 ISBN:9787510046469 版次:2 商品编码:11110551 包装:平装 外文名称:Geometric Invariant Theory Third Enlarged Edition 开本:24开 出版时间:2012-08-01 用纸:胶版纸 页数:292 正文语种:英文
In style this extra chapter is closer to the appendices added in the second edition than to the original text. In particular no proofs are given where satisfactory references exist.
1.Definitions
2.First properties
3.Good and bad actions
4.Further properties
5.Resume of some results of GRorrHENDIECK
Chapter 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
Chapter 2.Analysis of stability
1.A numeral criterion
2.The fiag complex
3.Applications
Chapter 3.An elementary example
1.Pre-stability
2.Stability
Chapter 4.Further examples
1.Binary quantics
2.Hypersurfaces
3.Counter-examples
4.Sequences of linear subspaces
5.The projective adjoint action
6.Space curves
Chapter 5.The problem of moduli-18t construction
1.General discussion
2.Moduli as an orbit space
3.First chern classes
4.Utilization of 4.6
Chapter 6.Abelian, schemes
1.Duals
2.Polarizations
3.Deformations
Chapter 7.The method of covan:ants-2nd construction
1.The technique
2.Moduli as an orbit space
3.The covariant
4.Application to curves
Chapter 8.The moment map
1.Symplectic geometry
2.Symplectic quotients and geometric invariant theory
3.Kahler and hyperkahler 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
几何不变量理论(第3版)(英文版) [Geometric Invariant Theory Third Enlarged Edition] 电子书 下载 mobi epub pdf txt
几何不变量理论(第3版)(英文版) [Geometric Invariant Theory Third Enlarged Edition]-so88
几何不变量理论(第3版)(英文版) [Geometric Invariant Theory Third Enlarged Edition] pdf epub mobi txt 电子书 下载 2022
图书介绍
☆☆☆☆☆
||
[美] 芒福德(Mumford D.) 著
出版社: 世界图书出版公司 ISBN:9787510046469 版次:2 商品编码:11110551 包装:平装 外文名称:Geometric Invariant Theory Third Enlarged Edition 开本:24开 出版时间:2012-08-01 用纸:胶版纸 页数:292 正文语种:英文
内容简介
This edition of the book has been extended to take account of one of these developments, one which was just hinted at in the second edition. A close and very fruitful relationship has been discovered between geometric invariant theory for quasi projective complex varieties and the moment map in Symplectic geometry, and a chapter has been added describing this relationship and some of its applications. In an infinite-dimensional setting the moment map links geometric invariant theory and Yang-Mills theory, which has of course been the focus of much attention among mathematicians over the last fifteen years.In style this extra chapter is closer to the appendices added in the second edition than to the original text. In particular no proofs are given where satisfactory references exist.
内页插图
目录
Chapter 0.Preliminaries1.Definitions
2.First properties
3.Good and bad actions
4.Further properties
5.Resume of some results of GRorrHENDIECK
Chapter 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
Chapter 2.Analysis of stability
1.A numeral criterion
2.The fiag complex
3.Applications
Chapter 3.An elementary example
1.Pre-stability
2.Stability
Chapter 4.Further examples
1.Binary quantics
2.Hypersurfaces
3.Counter-examples
4.Sequences of linear subspaces
5.The projective adjoint action
6.Space curves
Chapter 5.The problem of moduli-18t construction
1.General discussion
2.Moduli as an orbit space
3.First chern classes
4.Utilization of 4.6
Chapter 6.Abelian, schemes
1.Duals
2.Polarizations
3.Deformations
Chapter 7.The method of covan:ants-2nd construction
1.The technique
2.Moduli as an orbit space
3.The covariant
4.Application to curves
Chapter 8.The moment map
1.Symplectic geometry
2.Symplectic quotients and geometric invariant theory
3.Kahler and hyperkahler 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
前言/序言
几何不变量理论(第3版)(英文版) [Geometric Invariant Theory Third Enlarged Edition] 电子书 下载 mobi epub pdf txt
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