几何不变量理论（第3版）（英文版） [Geometric Invariant Theory Third Enlarged Edition] 下载 mobi epub pdf 电子书 2024

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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.

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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] 下载 mobi epub pdf txt 电子书 格式

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Mumford的早期著作

评分☆☆☆☆☆

这本书难度不小

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D.Mumford应该是几何方向的超级大牛了，他的红皮书是代数几何方向的必读教材。这本几何不变量理论研究了更深入的不变量理论，适合研究生阶段的阅读

评分☆☆☆☆☆

不妨买来一读, 必然会进步不小.

评分☆☆☆☆☆

不妨买来一读, 必然会进步不小.

评分☆☆☆☆☆

不妨买来一读, 必然会进步不小.

评分☆☆☆☆☆

不变量, 有着永恒的魅力, 人类永恒的追寻.

评分☆☆☆☆☆

不变量, 有着永恒的魅力, 人类永恒的追寻.

评分☆☆☆☆☆

书很好，慢慢看，我只是为了点豆豆，还没看

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