代数几何中的解析方法 (英文版)
Smm 1 surveys of modern mathematics
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328
九五品
库存2件
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
印刷时间2021-01
印次3
装帧精装
上书时间2022-08-10
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- 品相描述:九五品
图书标准信息
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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
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ISBN
9787040305319
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定价
48.00元
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装帧
精装
-
开本
16开
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纸张
胶版纸
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页数
231页
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字数
350千字
- 【内容简介】
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ThisvolumeisanexpansionoflecturesgivenbytheauthorattheParkCityMathematicsInstitutein2008aswellasinotherplaces.Themainpurposeofthebookistodescribeanalytictechniqueswhichareusefultostudyquestionssuchaslinearseries,multiplieridealsandvanishingtheoremsforalgebraicvectorbundles.Theexpositiontriestobeascondensedaspossible,assumingthatthereaderisalreadysomewhatacquaintedwiththebasicconceptspertainingtosheaftheory,homologicalalgebraandcomplexdifferentialgeometry.Inthefinalchapters,someveryrecentquestionsandopenproblemsareaddressed,forexampleresultsrelatedtothefinitenessofthecanonicalringandtheabundanceconjecture,aswellasresultsdescribingthegeometricstructureofKahlervarietiesandtheirpositivecones.
- 【目录】
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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
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