几何与分析（第2卷）

图书标准信息

• 作者 季理真 编
• 出版社 高等教育出版社
• 出版时间 2010-09
• 版次 1
• ISBN 9787040306613
• 定价 88.00元
• 装帧 精装
• 开本 16开
• 纸张 铜版纸
• 页数 563页
• 字数 800千字

【内容简介】

ThelaunchofthisAdvancedLecturesinMathematicsseriesisaimedatkeepingmathematiciansinformedofthelatestdevelopmentsinmathematics，aswellastoaidinthelearningofnewmathematicaltopicsbystudentsallovertheworld.Eachvolumeconsistsofeitheranexpositorymonographoracollectionofsignifycantintroductionstoimportanttopics，Thisseriesemphasizesthehistoryandsourcesofmotivationforthetopicsunderdiscussion，andalsogivesanoverviewofthecurrentstatusofresearchineachparticularfield.Thesevolumesarethefirstsourcetowhichpeoplewillturninordertolearnnewsubjectsandtodiscoverthelatestresultsofmanycutting-edgefieldsinmathematics.
Thisbookcontainsmanysubstantialpapersfromdistinguishedspeakersofaconference”GeometricAnalysis：PresentandFuture"andanoverviewoftheworksofProfessorShing-TungYau.ContributorsincludeE.Witten，Y.T.Siu，R.Hamilton，H.Hitchin，B.Lawson，A.Strominger，C.Vafa，W.Schmid，V.Guillemin，N.Mok，D.Christodoulou.Thisisavaluablereferencethatgivesanup-to-datedsummaryofgeometricanalysisanditsapplicationsinmanydifferentareasofmathematics.

【目录】

Part3MathematicalPhysics，AlgebraicGeometryandOtherTopics
TheCoherent-ConstructibleCorrespondenceandHomologicalMirrorSymmetryforToricVarieties
BohanFang，Chiu-ChuMelissaLiu，DavidTreumannandEricZaslow.
1Introduction
1.1Outline
2Mirrorsymmetryfortoricmanifolds
2.1Hori-Vafamirror
2.2Categoriesinmirrorsymmetry
2.3Resultstodate
3T-duality
3.1Momentpolytope
3.2Geometryoftheopenorbit
3.3Statementofsymplecticresults
3.4T-dualofanequivariantlinebundle
4Microlocalization
4.1Algebraicpreliminaries
4.2Thecastofcategories
4.3Fukaya-Ohtheorem
4.4Buildingtheequivalence
4.5Equivalenceandtheinversefunctor
4.6Singularsupportandcharacteristiccycles
4.7Commentsontechnicalities
4.8Statementofresults
5Coherent-constructiblecorrespondence
6Examples
6.1Takingthemappingcone
6.2ToricFanosurfaces
6.3Hirzebruchsurfaces
References
Superspace：aComfortablyVastAlgebraicVariety
T.Hiibsch
1Introduction
1.1Basicideasanddefinitions
1.2Thetraditionalsuperspace
2Off-shellworldlinesupermultiplets
2.1Adinkraicsupermultiplets
2.2Varioushangings
2.3Projectedsupermultiplets
2.4Supermultipletsvs.superfields
3Superspace，byconstruction
3.1Superpartnersoftime
3.2Atelescopingdeformationstructure
3.3Nontrivialsuperspacegeometry
3.4Higher-dimensionalspacetime
4Thecomfortablyvastsuperspace
References
AReportontheYau-ZaslowFormula
NaichungConanLeung
1Yau-Zaslowformulaanditsgeneralizations
2Yau-Zaslowapproach
3Matchingmethod
4Degenerationmethod
5Calabi-Yauthreefoldmethod
6Conclusions
References
Hermitian-Yang-MillsConnectionsonKahlerManifolds
JunLi
1Introduction
1.1Hermitian-Yang-Millsconnections
1.2HYMconnectionsleadtostablebundles
1.3Stablebundlesandtheirmodulispaces
1.4Flatbundlesandstablebundlesoncurves
2Donaldson-Uhlenbeck-Yautheorem
2.1Donaldsonsproofforalgebraicsurfaces
2.2Uhlenbeck-YausproofforKahlermanifolds
3Hermitian-Yang-Millsconnectionsoncurves
4Hermitian-Yang-Millsconnectionsonsurfaces
4.1ExtendingDUYcorrespondence
4.2Stabletopologyofthemodulispaces
4.3Donaldsonpolynomialinvariants
5HYMconnectionsonhighdimensionalvarieties
5.1ExtendingtheDUYcorrespondenceinhighdimensions
5.2Donaldson-Thomasinvariants
6Concludingremark
References~
AdditivityandRelativeKodairaDimensions
Tian-JunLiandWeiyiZhang
1Introduction
2KodairaDimensionsandfiberbundles
2.1hforcomplexmanifoldsanduptodimension3
2.2Ksforsymplectic4~manifolds
2.3Additivityforafiberbundle
3EmbeddedsymplecticsurfacesandrelativeKod.dim.indim.4.
3.1Embeddedsymplecticsurfacesandmaxinmlity
3.2Theadjointclass
3.3ExistenceandUniquenessofrelativelyminimalmodel
3.4（M，w，F)
4RelativeKod.dim.indim.2andfibrationsoverasurface
4.1（F，D)，Riemann-HurwitzformulaandSeifertfibrations...
4.2Lefschetzfibrations
References
DescendentIntegralsandTautologicalRingsof
ModuliSpacesofCurves
Kefen9LiuandHaoXu
1Introduction
2IntersectionnumbersandtheWitten-Kontsevichtheorem
2.1Witten-Kontsevichtheorem
2.2Virasoroconstraints
3Then-pointfunction
3.1Arecursiveformulaofn-pointfunctions
3.2Aneffectiverecursionformulaeofdescendentintegrals
4Hodgeintegrals
4.1Fabersalgorithm
4.2Hodgeintegralformulae
5HigherWeil-Peterssonvolumes
5.1GeneralizationofMirzakhanisrecursionformula
5.2RecursionformulaeofhigherWeil-Peterssonvolumes
6Fabersconjectureontautologicalrings
6.1TheFaberintersectionnumberconjecture
6.2Relationswithn-pointfunctions
7Dimensionoftautologicalrings
7.1Ramanujansmockthetafunctions
7.2Asymptoticsoftautologicaldimensions
8Gromov-Witteninvariants
8.1UniversalequationsofGromov-Witteninvariants
8.2Somevanishingidentities
9Wittensr-spinnumbers
9.1GeneralizedWittensconjecture
9.2AnalgorithmforcomputingWittensr-spinnumbers
References
AGeneralVoronoiSummationFormulaforGL（n，Z)
StephenD.MillerandWilfriedSehmid
1Introduction
2AutomorphicDistributions
3Vanishingtoinfiniteorder
4Classicalproofoftheformula
5Adelicproofoftheformula
References
GeometryofHolomorphicIsometriesandRelatedMaps
betweenBoundedDomains
NgaimingMok
1Examplesofholomorphicisometries
1.1Examplesofequivariantembeddingsintothe
projectivespace
1.2Non-standardholomorphicisometriesofthePoincar
diskintopolydisks
1.3Anon-standardholomorphicisometryofthePoincar
diskintoaSiegelupperhalf-plane
1.4Examplesofholomorphicisometrieswitharbitrary
normalizingconstantsA>1
2Analyticcontinuationofgermsofholomorphicisometries
2.1Analyticcontinuationofholomorphicisometriesintothe
projectivespaceequippedwiththeFubini-Studymetric
2.2Anextensionandrigidityproblemarisingfrom
commutatorsofmodularcorrespondences
2.3Analyticcontinuationofholomorphicisometriesupto
normalizingconstantswithrespecttotheBergman
metric-extensionbeyondtheboundary
2.4CanonicallyembeddableBergmanmanifoldsand
Bergmanmeromorphiccompactifications
3HolomorphicisometriesofthePoincardiskinto
boundedsymmetricdomains
3.1Structuralequationsonthenormofthesecond
fundamentalformandasymptoticvanishingorder
3.2HolomorphicisometriesofthePoincardiskinto
polydisks：structuralresults
3.3Calculatedexamplesonthenormofthesecond
fundamentalform
3.4HolomorphicisometriesofthePoincar5diskinto
polydisks：uniquenessresults
3.5Asymptotictotalgeodesyandapplications
4Measure-preservingalgebraiccorrespondencesonirreducible
boundedsymmetricdomains
4.1Statementsofresults
4.2Extensionresultsonstrictlypseudoconvex
algebraichypersurfaces
4.3Alexander-typeextensionresultsinthehigher-rankcase
4.4Totalgeodesyofgermsofmeasure-preservingholomorphie