代数几何中的解析方法

图书标准信息

• 作者 德马依（Jean Pierre Demailly） 著
• 出版社 高等教育出版社
• 出版时间 2010-09
• 版次 1
• ISBN 9787040305319
• 定价 48.00元
• 装帧 精装
• 开本 16开
• 纸张 胶版纸
• 页数 231页
• 字数 350千字

【内容简介】

ThisvolumeisanexpansionoflecturesgivenbytheauthorattheParkCityMathematicsInstitutein2008aswellasinotherplaces.Themainpurposeofthebookistodescribeanalytictechniqueswhichareusefultostudyquestionssuchaslinearseries，multiplieridealsandvanishingtheoremsforalgebraicvectorbundles.Theexpositiontriestobeascondensedaspossible，assumingthatthereaderisalreadysomewhatacquaintedwiththebasicconceptspertainingtosheaftheory，homologicalalgebraandcomplexdifferentialgeometry.Inthefinalchapters，someveryrecentquestionsandopenproblemsareaddressed，forexampleresultsrelatedtothefinitenessofthecanonicalringandtheabundanceconjecture，aswellasresultsdescribingthegeometricstructureofKahlervarietiesandtheirpositivecones.

【目录】

introduction
chapter1.preliminarymaterial：cohomology，currents
1.a.dolbeaultcohomologyandsheafcohomology
1.b.plurisubharmonicfunctions
1.c.positivecurrents

chapter2.lelongnumbersandintersectiontheory
2.a.multiplicationofcurrentsandmonge-ampereoperators
2.b.lelongnumbers

chapter3.hermitianvectorbundles，connectionsandcurvature
chapter4.bochnertechniqueandvanishingtheorems
4.a.laplace-beltramioperatorsandhodgetheory
4.b.serredualitytheorem
4.cbochner-kodaira-nakanoidentityonkahlermanifolds
4.d.vanishingtheorems

chapter5.l2estimatesandexistencetheorems
5.a.basicl2existencethcorcms
5.b.multiplieridealsheavesandnadelvanishingtheorem

chapter6.numericallyeffectiveandpseudo-effectivelinebundles
6.a.pseudo-effcctivelinebundlesandmetricswithminimalsingularities
6.b.neflinebundles
6.c.descriptionofthcpositivecones.
6.d.thekawamata-viehwegvanishingtheorem
6.e.auniformglobalgenerationpropertyduetoy.t.siu

chapter7.asimplealgebraicapproachtofujitasconjecture
chapter8.holomorphicmorseinequalities
8.a.generalanalyticstatementoncompactcomplexmanifolds
8.b.algebraiccounterpartsoftheholomorphicmorseinequalities
8.c.asymptoticcohomologygroups
8.d.transcendentalasymptoticcohomologyunctions

chapter9.effectiveversionofmatsusakasbigtheorem
chapter10.positivityconceptsforvectorbundles
chapter11.skodasl2estimatesforsurjectivebundlemorphisms
11.a.surjectivityanddivisiontheorems
11.b.applicationstolocalalgebra：thebriancon-skodatheorem

chapter12.theohsawa-takegoshil2extensiontheorem
12.a.thebasicaprioriinequality
12.b.abstractl2existencetheoremforsolutionsof0-equations
12.c.thel2extensiontheorem
12.d.skodasdivisiontheoremforidealsofholomorphicfunctions

chapter13.approximationofclosedpositivecurrentsbyanalyticcycles
13.a.approximationofplurisubharmonicfunctionsviabergmankernels
13.b.globalapproximationofclosed（1，1）-currentsonacompactcomplexmanifold
13.c.globalapproximationbydivisors
13.d.singularityexponentsandlogcanonicalthresholds
13.e.hodgeconjectureandapproximationof（p，p）-currents

chapter14.subadditivityofmultiplieridealsandfujitasapproximatezariskidecomposition
chapter15.hardlefschetztheorem
withmultiplieridealsheaves
15.a.abundlevaluedhardlefsehetztheorem
15.b.equisingularapproximationsofquasiplurisubharmonicfunctions
15.c.abochnertypeinequality
15.d.proofoftheorem15.1
15.e.acounterexample

chapter16.invarianceofplurigeneraofprojectivevarieties
chapter17.numericalcharacterizationofthekahlercone
17.a.positiveclassesinintermediate（p，p）-bidegrees
17.b.numericallypositiveclassesoftype（1，1）
17.c.deformationsofcompactkahlermanifolds

chapter18.structureofthepseudo-effectiveconeandmobileintersectiontheory
18.a.classesofmobilecurvesandofmobile（n-1，n-1）-currents
18.b.zariskidecompositionandmobileintersections
18.c.theorthogonalityestimate
18.d.dualofthepseudo-effectivecone
18.e.avolumeformulaforalgebraic（1，1）-classesonprojectivesurfaces

chapter19.super-canonicalmetricsandabundance
19.a.constructionofsuper-canonicalmetrics
19.b.invarianceofplurigeneraandpositivityofcurvatureofsuper-canonicalmetrics
19.c.tsujisstrategyforstudyingabundance
chapter20.siusanalyticapproachandpaunsnonvanishingtheorem
references