complex analytic and algebraic geometry

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1、ComplexAnalyticandDifferentialGeometryJean-PierreDemaillyUniversit´edeGrenobleIInstitutFourier,UMR5582duCNRS38402Saint-Martind’H`eres,FranceTypesetonSaturdayJune9,2007TableofContentsForeword...................................................4pI.BasicConceptsofComplexGeometry...............

2、.65p§1.DifferentialCalculusonManifolds....................1§2.CurrentsonDifferentiableManifolds..................8§3.HolomorphicFunctionsandComplexManifolds........16§4.SubharmonicFunctions..............................26§5.PlurisubharmonicFunctions..........................35§6.DomainsofHo

3、lomorphyandSteinManifolds...........43§7.PseudoconvexOpenSetsinCn.......................52§8.Exercises..........................................60II.CoherentSheavesandComplexAnalyticSpaces......70p§1.TheLocalRingofGermsofAnalyticFunctions........1§2.PresheavesandSheaves...................

4、..........6§3.CoherentSheaves...................................10§4.ComplexAnalyticSets.LocalProperties..............19§5.ComplexSpaces....................................32§6.MeromorphicFunctionsandAnalyticCycles...........43§7.NormalSpacesandNormalization....................52§8.Holomo

5、rphicMappingsandExtensionTheorems.......56§9.MeromorphicMaps,ModificationsandBlow-ups........61§10.AlgebraicandAnalyticSchemes......................65§11.Exercises..........................................67III.PositiveCurrentsandPotentialTheory...............110p§1.BasicConceptsofPositivi

6、ty..........................1§2.ClosedPositiveCurrents.............................11§3.Monge-Amp`ereOperators...........................18§4.ExtendedMonge-Amp`ereOperators..................254TableofContents§5.LelongNumbers....................................33§6.TheLelong-JensenFormula.

7、.........................38§7.ComparisonTheoremsforLelongNumbers............43§8.Siu’sSemicontinuityTheorem........................51§9.LelongNumbersofDirectImageCurrents.............61§10.ASchwarzLemma.ApplicationtoNumberTheory.....69§11.Capacities,RegularityandCap