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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.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

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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不变量真的是好神奇的存在。专业英文书籍的引进，真是帮了很多学者的忙了

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编辑本段

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对于一般的代数群，其不变量理论与线性代数、二次型及行列式理论密切相关。

评分☆☆☆☆☆

不变量, 有着永恒的魅力, 人类永恒的追寻.

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大卫·蒙福德在1960年代创建了几何不变量理论，这是构造模空间的有力工具。此理论探讨代数簇在群作用下的商空间，并研究轨道的几何性质。几何不变量理论与古典不变量理论的关联如次：考虑域 k 上的仿射代数簇 X = SpecA，群 G 作用其上，则商空间 X / G 也是仿射代数簇，其坐标环即不变量环 AG。希尔伯特证明若 G 是一般线性群，则 AG 是有限生成 k-代数；此结果对一般的约化群依然成立，然而 X / G 可能有颇复杂的几何性质，也未必满足商对象应满足的范畴论性质。由于Bn(K)是 Zn(K)的子群，把商群Zn(K)/Bn(K)叫做单纯复形K的n维（下）同调群，记作Hn(K)。Hn(K)中的每一个元素叫做一个n维同调类。如果两个n维闭链zń,z怽的差为一个边缘链时,就叫zń与z怽同调。如果zn是边缘链，则称zn同调于零。例如,图8b中的单纯复形,2个一维闭链(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┡))。因而这两个闭链同调（而它们都不同调于零）。同调群 Hn(K)的秩叫做K的n维贝蒂数。如果在n维链群的定义中,用任意的一个交换群G中的元素代替整数，可以得到以G为系数的n维链群 Cn(K;G)。相似地有以G为系数的n维边缘群Bn(K;G),n维闭链群Zn(K;G)。由此定义以G为系数的n维同调群Hn(K;G)。

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不妨买来一读, 必然会进步不小.

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不妨买来一读, 必然会进步不小.

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多面体

评分☆☆☆☆☆

不妨买来一读, 必然会进步不小.

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