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1、H.Grauert?Th.Peternell?R.Remmert(Eds.)VSeveralComplexVariablesVIISheaf-TheoreticalMethodsinComplexAnalysisSpringer-VerlagBerlinHeidelbergNewYorkLondonParisTokyoHongKongBarcelonaBudapestEncyclopaediaofMathematicalSciencesVolume7426246+%B^^Editor-in-Chief:R.V
2、GamkrelidzeContentsIntroduction1ChapterI.LocalTheoryofComplexSpacesR.Remmert7ChapterII.DifferentialCalculus,HolomorphicMapsandLinearStructuresonComplexSpacesTh.PeternellandR.Remmert97ChapterIII.CohomologyTh.Peternell145ChapterIV.SeminormalComplexSpacesG.Det
3、hloffandH.Grauert183ChapterV.Pseudoconvexity,theLeviProblemandVanishingTheoremsTh.Peternell221ChapterVI.Theoryof#-Convexityand^-ConcavityH.Grauert259ChapterVII.ModificationsTh.Peternell285ChapterVIII.CycleSpacesF.CampanaandTh.Petemell319ChapterIX.Extensiono
4、fAnalyticObjectsH.GrauertandR.Remmert351AuthorIndex361SubjectIndex363IntroductionOfmakingmanybooksthereisnoend;andmuchstudyisawearinessoftheflesh.Eccl.12.12.1.InthebeginningRiemanncreatedthesurfaces.Theperiodsofintegralsofabeliandifferentialsonacompactsurfa
5、ceofgenusgimmediatelyattachag-dimensionalcomplextorustoX.Ifg>2,themodulispaceofXdependson3g—3complexparameters.Thusproblemsinonecomplexvariablelead,fromtheverybeginning,tostudiesinseveralcomplexvariables.Complextoriandmodulispacesarecomplexmanifolds,i.e.Hau
6、sdorffspaceswithlocalcomplexcoordinateszx,...,z?;holomorphicfunctionsare,locally,thosefunctionswhichareholomorphicinthesecoordinates.Inthesecondhalfofthe19thcentury,classicalalgebraicgeometrywasborninItaly.Theobjectsaresetsofcommonzerosofpolynomials.Suchset
7、sareoffinitedimension,butmayhavesingularitiesformingaclosedsubsetoflowerdimension;outsideofthesingularlocusthesezerosetsarecomplexmanifolds.Evenifonewantstostudycomplexmanifoldsonly,singularitiesdooccurimmediately:ThefibersofholomorphicmapsX-*Ybetweencomple
8、xmanifoldsareanalyticsetsinX,i.e.closedsubsetswhichare,locally,zerosetsoffinitelymanyholomorphicfunctions.Analyticsetsarecomplexmanifoldsoutsideoftheirsingularlocusonly:Asimpleexampleofafiberwithsingul
