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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

評分☆☆☆☆☆

大衛·濛福德在1960年代創建瞭幾何不變量理論，這是構造模空間的有力工具。此理論探討代數簇在群作用下的商空間，並研究軌道的幾何性質。幾何不變量理論與古典不變量理論的關聯如次：考慮域 k 上的仿射代數簇 X = SpecA，群 G 作用其上，則商空間 X / G 也是仿射代數簇，其坐標環即不變量環 AG。希爾伯特證明若 G 是一般綫性群，則 AG 是有限生成 k-代數；此結果對一般的約化群依然成立，然而 X / G 可能有頗復雜的幾何性質，也未必滿足商對象應滿足的範疇論性質。由於Bn(K)是 Zn(K)的子群，把商群Zn(K)/Bn(K)叫做單純復形K的n維（下）同調群，記作Hn(K)。Hn(K)中的每一個元素叫做一個n維同調類。如果兩個n維閉鏈zń,z怽的差為一個邊緣鏈時,就叫zń與z怽同調。如果zn是邊緣鏈，則稱zn同調於零。例如,圖8b中的單純復形,2個一維閉鏈(A,B)+(C,A)+(B,C)，(A┡,B┡)+(C┡,A┡)+(B┡,C┡)有嬠((A,B,A┡)+(A┡,B,B┡)+(B,C,B┡)-(C,B┡,C┡)-(C,C┡,A┡)-(C,A┡,A))=((A,B)+(C,A)+(B,C))-((A┡,B┡)+(C┡,A┡)+(B┡,C┡))。因而這兩個閉鏈同調（而它們都不同調於零）。同調群 Hn(K)的秩叫做K的n維貝蒂數。如果在n維鏈群的定義中,用任意的一個交換群G中的元素代替整數，可以得到以G為係數的n維鏈群 Cn(K;G)。相似地有以G為係數的n維邊緣群Bn(K;G),n維閉鏈群Zn(K;G)。由此定義以G為係數的n維同調群Hn(K;G)。

評分☆☆☆☆☆

不妨買來一讀, 必然會進步不小.

評分☆☆☆☆☆

多好的書啊, 值得好哈看看

評分☆☆☆☆☆

不變量, 有著永恒的魅力, 人類永恒的追尋.

評分☆☆☆☆☆

早就想買來看瞭。。。

評分☆☆☆☆☆

書很好，慢慢看，我隻是為瞭點豆豆，還沒看

評分☆☆☆☆☆

不變量, 有著永恒的魅力, 人類永恒的追尋.

評分☆☆☆☆☆

Mumford的早期著作

評分☆☆☆☆☆

不變量真的是好神奇的存在。專業英文書籍的引進，真是幫瞭很多學者的忙瞭

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