內容簡介
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.
內頁插圖
目錄
Chapter 0.Preliminaries
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
前言/序言
幾何不變量理論(第3版)(英文版) [Geometric Invariant Theory Third Enlarged Edition] 下載 mobi epub pdf txt 電子書 格式
幾何不變量理論(第3版)(英文版) [Geometric Invariant Theory Third Enlarged Edition] 下載 mobi pdf epub txt 電子書 格式 2025
評分
☆☆☆☆☆
對我很有用,很喜歡,是介紹具體的不變量內容的書
評分
☆☆☆☆☆
不變量, 有著永恒的魅力, 人類永恒的追尋.
評分
☆☆☆☆☆
對於有限群,不變量理論與伽羅瓦理論有密切聯係,一個較早的結果涉及瞭對稱群 Sn 在多項式環 上的作用:Sn 作用下的不變量構成一個子環,由基本對稱多項式生成,由於基本對稱多項式彼此代數獨立,此不變量環本身也同構於另一多項式環。Chevalley-Shephard-Todd 定理刻劃瞭其不變量環同構於多項式環的有限群。最近的研究則更關切算法問題,例如計算不變量環的生成元,或給齣其次數的上界。
評分
☆☆☆☆☆
連續映射導齣的同態
評分
☆☆☆☆☆
單純映射 給定瞭兩個單純復形K,L,且指定瞭K的每一個頂點(0維單形)到L的某個頂點的一個對應,並把K中的屬於同一個單形的所有頂點對應到L的同在一個單形中的頂點,這個對應叫從K到L的單純映射。單純映射ƒ:K→L把 K中的每一個定嚮單形(頂點的一個順序)映射到L中的一個定嚮單形(得到對應頂點的一個順序,若有兩個頂點的像重閤,則理解為對應到0),由此産生瞭一個從Cn(K;G)到 Cn(L;G)的同態,並且可以證明它把Zn(K;G)映射到Zn(L;G),Bn(K;G)映射到Bn(L;G)。從這個同態可以導齣一個從Hn(K;G)到Hn(L;G)的同態。
評分
☆☆☆☆☆
影印版的書,僅供專業人員參考。
評分
☆☆☆☆☆
不變量, 有著永恒的魅力, 人類永恒的追尋.
評分
☆☆☆☆☆
對於有限群,不變量理論與伽羅瓦理論有密切聯係,一個較早的結果涉及瞭對稱群 Sn 在多項式環 上的作用:Sn 作用下的不變量構成一個子環,由基本對稱多項式生成,由於基本對稱多項式彼此代數獨立,此不變量環本身也同構於另一多項式環。Chevalley-Shephard-Todd 定理刻劃瞭其不變量環同構於多項式環的有限群。最近的研究則更關切算法問題,例如計算不變量環的生成元,或給齣其次數的上界。
評分
☆☆☆☆☆
這個是非常棒的商品哦。
幾何不變量理論(第3版)(英文版) [Geometric Invariant Theory Third Enlarged Edition] mobi epub pdf txt 電子書 格式下載 2025