几何不变量理论（第3版）（英文版）

图书标准信息

• 作者 [美]芒福德（Mumford D.） 著
• 出版社 世界图书出版公司
• 出版时间 2012-08
• 版次 2
• ISBN 9787510046469
• 定价 49.00元
• 装帧 平装
• 开本 24开
• 纸张 胶版纸
• 页数 292页
• 正文语种 英语

【内容简介】

Thiseditionofthebookhasbeenextendedtotakeaccountofoneofthesedevelopments，onewhichwasjusthintedatinthesecondedition.AcloseandveryfruitfulrelationshiphasbeendiscoveredbetweengeometricinvarianttheoryforquasiprojectivecomplexvarietiesandthemomentmapinSymplecticgeometry，andachapterhasbeenaddeddescribingthisrelationshipandsomeofitsapplications.Inaninfinite-dimensionalsettingthemomentmaplinksgeometricinvarianttheoryandYang-Millstheory，whichhasofcoursebeenthefocusofmuchattentionamongmathematiciansoverthelastfifteenyears.
Instylethisextrachapterisclosertotheappendicesaddedinthesecondeditionthantotheoriginaltext.Inparticularnoproofsaregivenwheresatisfactoryreferencesexist.

【目录】

Chapter0.Preliminaries
1.Definitions
2.Firstproperties
3.Goodandbadactions
4.Furtherproperties
5.ResumeofsomeresultsofGRorrHENDIECK

Chapter1.Fundamentaltheoremsfortheactionsofreductivegroups
1.Definitions
2.Theaffinecase
3.Linearizationofaninvertiblesheaf
4.Thegeneralcase
5.Functionalproperties

Chapter2.Analysisofstability
1.Anumeralcriterion
2.Thefiagcomplex
3.Applications

Chapter3.Anelementaryexample
1.Pre-stability
2．Stability

Chapter4.Furtherexamples
1.Binaryquantics
2.Hypersurfaces
3.Counter-examples
4.Sequencesoflinearsubspaces
5.Theprojectiveadjointaction
6.Spacecurves

Chapter5.Theproblemofmoduli-18tconstruction
1.Generaldiscussion
2.Moduliasanorbitspace
3.Firstchernclasses
4.Utilizationof4.6

Chapter6.Abelian，schemes
1．Duals
2.Polarizations
3.Deformations

Chapter7.Themethodofcovan：ants-2ndconstruction
1.Thetechnique
2.Moduliasanorbitspace
3.Thecovariant
4.Applicationtocurves

Chapter8.Themomentmap
1.Symplecticgeometry
2.Symplecticquotientsandgeometricinvarianttheory
3.Kahlerandhyperkahlerquotients
4.Singularquotients
5.Geometryofthemomentmap
6.Thecohomologyofquotients：thesymplecticcase
7.Thecohomologyofquotients：thealgebraiccase
8.VectorbundlesandtheYang-Millsfunctional
9.Yang-MillstheoryoverRiemannsurfaces

AppendixtoChapter1
AppendixtoChapter2
AppendixtoChapter3
AppendixtoChapter4
AppendixtoChapter5
AppendixtoChapter7
References
Indexofdefinitionsandnotations