幾何不變量理論（第3版）（英文版） [Geometric Invariant Theory Third Enlarged Edition] pdf epub mobi txt 电子书 下载 2025

☆☆☆☆☆

[美] 芒福德（Mumford D.） 著

出版社： 世界图书出版公司

ISBN：9787510046469

版次：2

商品编码：11110551

包装：平装

外文名称：Geometric Invariant Theory Third Enlarged Edition

开本：24开

出版时间：2012-08-01

用纸：胶版纸

页数：292

正文语种：英文

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

评分☆☆☆☆☆

不妨买来一读, 必然会进步不小.

评分☆☆☆☆☆

书质量不错，字体比较小，Mumford主页上自己做了个扫描版，质量不错。

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☆☆☆☆☆

先说外观 不错 包装很好装订的也不错 字体大小适中 感觉很舒服 内容 很博大 涉及很多很多 真的是对一个人知识面理解力的考验 要细细的读 不断的品 现在还没读完 但是 依然推荐

评分☆☆☆☆☆

好书好书经典经典，居家旅行必备！没有的赶紧收藏，绝版就找不到了！

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☆☆☆☆☆

书质量不错，字体比较小，Mumford主页上自己做了个扫描版，质量不错。