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

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

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

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] epub pdf mobi txt 电子书 下载 2024

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

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☆☆☆☆☆

不变量, 有着永恒的魅力, 人类永恒的追寻.

评分☆☆☆☆☆

不妨买来一读, 必然会进步不小.

评分☆☆☆☆☆

影印版的书，仅供专业人员参考。

评分☆☆☆☆☆

给了两个多面体|K|、|L|之间的一个连续映射F：│K│→│L│，可以将K适当重分成另一复形K┡,并用一个单纯映射去逼近F。利用这个单纯映射导出的同调群之间的同态得到Hn(│K┡│；G)到Hn(│L│；G)的同态，并且可以证明，Hn(│K┡│；G)与Hn(|K|;G)自然地同构。 于是记此同态为Fn：Hn(|K|;G)→Hn(│L│;G)。

评分☆☆☆☆☆

讲了 几何不变量

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