complex analytic and differential geometry - j. demailly

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1、ComplexAnalyticandDierentialGeometryean-ierreDemaillyUniversitedeGrenoble

nstitutFourier,UR5582duCRS38402Saint-artind'Heres,FranceTypesetonFridayctober3,1997TableofContentsForeword...................................................4p
.BasicConceptsofComplexGeometry................65px1.Di

2、erentialCalculusonanifolds....................1x2.CurrentsonDierentiableanifolds..................8x3.HolomorphicFunctionsandComplexanifolds........16x4.SubharmonicFunctions..............................26x5.lurisubharmonicFunctions..........................35x6.DomainsofHolomorphyandSteinanif

3、olds...........43nx7.seudoconvexpenSetsinC.......................52x8.Exercises..........................................60

.CoherentSheavesandComplexAnalyticSpaces......70px1.TheocalRingofGermsofAnalyticFunctions........1x2.resheavesandSheaves.............................6x3.CoherentSheaves...

4、................................10x4.ComplexAnalyticSets.ocalroperties..............19x5.ComplexSpaces....................................32x6.eromorphicFunctionsandAnalyticCycles...........43x7.ormalSpacesandormalization....................52x8.HolomorphicappingsandExtensionTheorems.......56x

5、9.eromorphicaps,odicationsandBlow-ups........61x10.AlgebraicandAnalyticSchemes......................65x11.Exercises..........................................67


.ositiveCurrentsandotentialTheory...............10px1.BasicConceptsofositivity..........................1x2.ClosedositiveCurrents.

6、............................11x3.onge-Ampereperators...........................18x4.Extendedonge-Ampereperators..................25x5.elongumbers....................................33x6.Theelong-ensenFormula..........................38x7.ComparisonTheoremsforelongumbers............43x8.S

7、iu'sSemicontinuityTheorem........................514TableofContentsx9.elongumbersofDirect
mageCurrents.............61x10.ASchwarzemma.ApplicationtoumberTheory.....69x11.Capacities,RegularityandCap