复几何导论

图书标准信息

• 作者 [德]霍布西兹 著
• 出版社 世界图书出版公司
• 出版时间 2010-01
• 版次 1
• ISBN 9787510004636
• 定价 39.00元
• 装帧 平装
• 开本 24开
• 纸张 胶版纸
• 页数 309页
• 正文语种 英语
• 原版书名 Complex Geometry: An Introduction

【内容简介】

Complexgeometryisahighlyattractivebranchofmodernmathematicsthathaswitnessedmanyyearsofactiveandsuccessfulresearchandthathasre-centlyobtainednewimpetusfromphysicistsinterestinquestionsrelatedtomirrorsymmetry.Duetoitsinteractionswithvariousotherfields(differential,algebraic,andarithmeticgeometry,butalsostringtheoryandconformalfieldtheory),ithasbecomeanareawithmanyfacets.Also,thereareanumberofchallengingopenproblemswhichcontributetothesubjectsattraction.ThemostfamousamongthemistheHodgeconjecture,oneofthesevenone-milliondollarmillenniumproblemsoftheClayMathematicsInstitute.So,itseemslikelytatthisareawillfascinatenewgenerationsformanyyearstocome.

【目录】

1LocalTheory
1.1HolomorphicFunctionsofSeveralVariables
1.2ComplexandHermitianStructures
1.3DifferentialForms
2ComplexManifolds
2.1ComplexManifolds:DefinitionandExamples
2.2HolomorphicVectorBundles
2.3DivisorsandLineBundles
2.4TheProjectiveSpace
2.5Blow-ups
2.6DifferentialCalculusonComplexManifolds
3KahlerManifolds
3.1KahlerIdentities
3.2HodgeTheoryonKahlerManifolds
3.3LefschetzTheorems
Appendix
3.AFormalityofCompactKahlerManifolds
3.BSUSYforKahlerManifolds
3.CHodgeStructures
4VectorBundles
4.1HermitianVectorBundlesandSerreDuality
4.2Connections
4.3Curvature
4.4ChernClasses
Appendix
4.ALevi-CivitaConnectionandHolonomyonComplexManifolds
4.BHermite-EinsteinandKahler-EinsteinMetrics
5ApplicationsofCohomology
5.1Hirzebruch-Riemann-RochTheorem
5.2KodairaVanishingTheoremandApplications
5.3KodairaEmbeddingTheorem
DeformationsofComplexStructures
6.1TheMaurer-CartanEquation
6.2GeneralResults
Appendix
6.AdGBV-Algebras
AHodgeTheoryonDifferentiableManifolds
BSheafCohomology
References
Index