EMS__Several_Complex_Variables_04 .pdf

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1、S.G.GindikinG.M.Khenkin(Eds.)SeveralComplexVariablesIVAlgebraicAspectsofComplexAnalysisSpringer-VerlagBerlinHeidelbergNewYorkLondonParisTokyoHongKongContentsI.MethodsintheTheoryofSheavesandSteinSpacesA.L.Onishchik1II.HolomorphicVectorBundlesandtheOka-GrauertPrincipleJ.Leiterer63III.De

2、formationsofComplexSpacesV.P.Palamodov105IV.HomogeneousComplexManifoldsD.N.Akhiezer195AuthorIndex245SubjectIndex248I.MethodsintheTheoryofSheavesandSteinSpacesA.L.OnishchikTranslatedfromtheRussianbyJ.NunemacherContentsIntroduction2Chapter1.Sheaves31.DefinitionofaSheaf32.SheavesofGermso

3、fFunctions;Presheaves43.TheSimplestConceptsRelatedtoSheavesofGroups,Algebras,andModules64.TheLiftingofSections85.TheExtensionofSections116.DirectandInverseImages12Chapter2.ComplexSpaces131.AnalyticLocalAlgebras132.AnalyticSets153.RingedSpaces164.CoherentSheavesofModules185.AnalyticSpa

4、ces206.NormalSpaces237.ConstructionsofComplexSpaces258.HolomorphicFiberBundles269.MeromorphicFunctionsandDivisors28Chapter3.CohomologywithValuesinaSheaf291.TheObstructiontotheLiftingofaSection302.SimplicialStructuresandCechCohomology312A.L.Onishchik3.BasicPropertiesofCohomology334.The

5、CalculationofCohomologyUsingResolutions345.ComplexesofDifferentialForms366.TheCousinTheorems397.CohomologywithValuesinaSheafofNonabelianGroups41Chapter4.SteinSpaces431.DefinitionandExamplesofSteinSpaces432.TheTheoremsofCartan463.FurtherExamplesandConstructionsofSteinSpaces494.TheProbl

6、emsofCousinandPoincare505.TopologicalProperties526.ImbeddingsintoAffineSpace527.HolomorphicFiberBundleswithSteinBaseandFiber538.SteinAlgebras559.HolomorphicallyConvexSpaces56Bibliography57IntroductionThisarticleisdevotedtocohomologicalmethodsincomplexanalysis,whichhaveundergoneintensi

7、vedevelopmentinthecourseofthelast35years.Thebasicobjectofstudyhereisacomplexanalyticspaceor,roughlyspeaking,acomplexanalyticmanifoldwithsingularpoints.Analyticspacesbelong(asdoalsoanalyticanddifferentiablemanifolds,supermanifolds,andalgebraicvarieties)totheclassofmathematicalstructure

8、swhic