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

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☆☆☆☆☆

[美] 芒福德（Mumford D.） 著

齣版社： 世界圖書齣版公司

ISBN：9787510046469

版次：2

商品編碼：11110551

包裝：平裝

外文名稱：Geometric Invariant Theory Third Enlarged Edition

開本：24開

齣版時間：2012-08-01

用紙：膠版紙

頁數：292

正文語種：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

評分☆☆☆☆☆

早就想買來看瞭。。。

評分☆☆☆☆☆

不妨買來一讀, 必然會進步不小.

評分☆☆☆☆☆

D.Mumford應該是幾何方嚮的超級大牛瞭，他的紅皮書是代數幾何方嚮的必讀教材。這本幾何不變量理論研究瞭更深入的不變量理論，適閤研究生階段的閱讀

評分☆☆☆☆☆

不妨買來一讀, 必然會進步不小.

評分☆☆☆☆☆

幾何都比較有意思，比較有意思

評分☆☆☆☆☆

不妨買來一讀, 必然會進步不小.

評分☆☆☆☆☆

不變量, 有著永恒的魅力, 人類永恒的追尋.

評分☆☆☆☆☆

不變量, 有著永恒的魅力, 人類永恒的追尋.

評分☆☆☆☆☆

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