EMS__Several_Complex_Variables_07 .pdf

《EMS__Several_Complex_Variables_07 .pdf》由会员上传分享，免费在线阅读，更多相关内容在学术论文-天天文库。

1、H.Grauert?Th.Peternell?R.Remmert(Eds.)VSeveralComplexVariablesVIISheaf-TheoreticalMethodsinComplexAnalysisSpringer-VerlagBerlinHeidelbergNewYorkLondonParisTokyoHongKongBarcelonaBudapestEncyclopaediaofMathematicalSciencesVolume7426246+%B^^Editor-in-Chief:R.VGamkrelidzeContentsIntroduction1Chapte

2、rI.LocalTheoryofComplexSpacesR.Remmert7ChapterII.DifferentialCalculus,HolomorphicMapsandLinearStructuresonComplexSpacesTh.PeternellandR.Remmert97ChapterIII.CohomologyTh.Peternell145ChapterIV.SeminormalComplexSpacesG.DethloffandH.Grauert183ChapterV.Pseudoconvexity,theLeviProblemandVanishingTheor

3、emsTh.Peternell221ChapterVI.Theoryof#-Convexityand^-ConcavityH.Grauert259ChapterVII.ModificationsTh.Peternell285ChapterVIII.CycleSpacesF.CampanaandTh.Petemell319ChapterIX.ExtensionofAnalyticObjectsH.GrauertandR.Remmert351AuthorIndex361SubjectIndex363IntroductionOfmakingmanybooksthereisnoend;and

4、muchstudyisawearinessoftheflesh.Eccl.12.12.1.InthebeginningRiemanncreatedthesurfaces.Theperiodsofintegralsofabeliandifferentialsonacompactsurfaceofgenusgimmediatelyattachag-dimensionalcomplextorustoX.Ifg>2,themodulispaceofXdependson3g—3complexparameters.Thusproblemsinonecomplexvariablelead,from

5、theverybeginning,tostudiesinseveralcomplexvariables.Complextoriandmodulispacesarecomplexmanifolds,i.e.Hausdorffspaceswithlocalcomplexcoordinateszx,...,z?;holomorphicfunctionsare,locally,thosefunctionswhichareholomorphicinthesecoordinates.Inthesecondhalfofthe19thcentury,classicalalgebraicgeometr

6、ywasborninItaly.Theobjectsaresetsofcommonzerosofpolynomials.Suchsetsareoffinitedimension,butmayhavesingularitiesformingaclosedsubsetoflowerdimension;outsideofthesingularlocusthesezerosetsarecomplexmanifolds.Evenifonewantstostudycomplexmanifoldsonly,singularitiesdooccurimmediately:Thefibersofhol

7、omorphicmapsX-*YbetweencomplexmanifoldsareanalyticsetsinX,i.e.closedsubsetswhichare,locally,zerosetsoffinitelymanyholomorphicfunctions.Analyticsetsarecomplexmanifoldsoutsideoftheirsingularlocusonly:Asimpleexampleofafiberwithsingul