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季理真 编 / 高等教育出版社 / 2010-09 / 精装
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几何与分析(第2卷)
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.
Part3MathematicalPhysics,AlgebraicGeometryandOtherTopicsTheCoherent-ConstructibleCorrespondenceandHomologicalMirrorSymmetryforToricVarietiesBohanFang,Chiu-ChuMelissaLiu,DavidTreumannandEricZaslow.1Introduction1.1Outline2Mirrorsymmetryfortoricmanifolds2.1Hori-Vafamirror2.2Categoriesinmirrorsymmetry2.3Resultstodate3T-duality3.1Momentpolytope3.2Geometryoftheopenorbit3.3Statementofsymplecticresults3.4T-dualofanequivariantlinebundle4Microlocalization4.1Algebraicpreliminaries4.2Thecastofcategories4.3Fukaya-Ohtheorem4.4Buildingtheequivalence4.5Equivalenceandtheinversefunctor4.6Singularsupportandcharacteristiccycles4.7Commentsontechnicalities4.8Statementofresults5Coherent-constructiblecorrespondence6Examples6.1Takingthemappingcone6.2ToricFanosurfaces6.3HirzebruchsurfacesReferencesSuperspace:aComfortablyVastAlgebraicVarietyT.Hiibsch1Introduction1.1Basicideasanddefinitions1.2Thetraditionalsuperspace2Off-shellworldlinesupermultiplets2.1Adinkraicsupermultiplets2.2Varioushangings2.3Projectedsupermultiplets2.4Supermultipletsvs.superfields3Superspace,byconstruction3.1Superpartnersoftime3.2Atelescopingdeformationstructure3.3Nontrivialsuperspacegeometry3.4Higher-dimensionalspacetime4ThecomfortablyvastsuperspaceReferencesAReportontheYau-ZaslowFormulaNaichungConanLeung1Yau-Zaslowformulaanditsgeneralizations2Yau-Zaslowapproach3Matchingmethod4Degenerationmethod5Calabi-Yauthreefoldmethod6ConclusionsReferencesHermitian-Yang-MillsConnectionsonKahlerManifoldsJunLi1Introduction1.1Hermitian-Yang-Millsconnections1.2HYMconnectionsleadtostablebundles1.3Stablebundlesandtheirmodulispaces1.4Flatbundlesandstablebundlesoncurves2Donaldson-Uhlenbeck-Yautheorem2.1Donaldsonsproofforalgebraicsurfaces2.2Uhlenbeck-YausproofforKahlermanifolds3Hermitian-Yang-Millsconnectionsoncurves4Hermitian-Yang-Millsconnectionsonsurfaces4.1ExtendingDUYcorrespondence4.2Stabletopologyofthemodulispaces4.3Donaldsonpolynomialinvariants5HYMconnectionsonhighdimensionalvarieties5.1ExtendingtheDUYcorrespondenceinhighdimensions5.2Donaldson-Thomasinvariants6ConcludingremarkReferences~AdditivityandRelativeKodairaDimensionsTian-JunLiandWeiyiZhang1Introduction2KodairaDimensionsandfiberbundles2.1hforcomplexmanifoldsanduptodimension32.2Ksforsymplectic4~manifolds2.3Additivityforafiberbundle3EmbeddedsymplecticsurfacesandrelativeKod.dim.indim.4.3.1Embeddedsymplecticsurfacesandmaxinmlity3.2Theadjointclass3.3ExistenceandUniquenessofrelativelyminimalmodel3.4(M,w,F)4RelativeKod.dim.indim.2andfibrationsoverasurface4.1(F,D),Riemann-HurwitzformulaandSeifertfibrations...4.2LefschetzfibrationsReferencesDescendentIntegralsandTautologicalRingsofModuliSpacesofCurvesKefen9LiuandHaoXu1Introduction2IntersectionnumbersandtheWitten-Kontsevichtheorem2.1Witten-Kontsevichtheorem2.2Virasoroconstraints3Then-pointfunction3.1Arecursiveformulaofn-pointfunctions3.2Aneffectiverecursionformulaeofdescendentintegrals4Hodgeintegrals4.1Fabersalgorithm4.2Hodgeintegralformulae5HigherWeil-Peterssonvolumes5.1GeneralizationofMirzakhanisrecursionformula5.2RecursionformulaeofhigherWeil-Peterssonvolumes6Fabersconjectureontautologicalrings6.1TheFaberintersectionnumberconjecture6.2Relationswithn-pointfunctions7Dimensionoftautologicalrings7.1Ramanujansmockthetafunctions7.2Asymptoticsoftautologicaldimensions8Gromov-Witteninvariants8.1UniversalequationsofGromov-Witteninvariants8.2Somevanishingidentities9Wittensr-spinnumbers9.1GeneralizedWittensconjecture9.2AnalgorithmforcomputingWittensr-spinnumbersReferencesAGeneralVoronoiSummationFormulaforGL(n,Z)StephenD.MillerandWilfriedSehmid1Introduction2AutomorphicDistributions3Vanishingtoinfiniteorder4Classicalproofoftheformula5AdelicproofoftheformulaReferencesGeometryofHolomorphicIsometriesandRelatedMapsbetweenBoundedDomainsNgaimingMok1Examplesofholomorphicisometries1.1Examplesofequivariantembeddingsintotheprojectivespace1.2Non-standardholomorphicisometriesofthePoincardiskintopolydisks1.3Anon-standardholomorphicisometryofthePoincardiskintoaSiegelupperhalf-plane1.4ExamplesofholomorphicisometrieswitharbitrarynormalizingconstantsA>12Analyticcontinuationofgermsofholomorphicisometries2.1AnalyticcontinuationofholomorphicisometriesintotheprojectivespaceequippedwiththeFubini-Studymetric2.2Anextensionandrigidityproblemarisingfromcommutatorsofmodularcorrespondences2.3AnalyticcontinuationofholomorphicisometriesuptonormalizingconstantswithrespecttotheBergmanmetric-extensionbeyondtheboundary2.4CanonicallyembeddableBergmanmanifoldsandBergmanmeromorphiccompactifications3HolomorphicisometriesofthePoincardiskintoboundedsymmetricdomains3.1Structuralequationsonthenormofthesecondfundamentalformandasymptoticvanishingorder3.2HolomorphicisometriesofthePoincardiskintopolydisks:structuralresults3.3Calculatedexamplesonthenormofthesecondfundamentalform3.4HolomorphicisometriesofthePoincar5diskintopolydisks:uniquenessresults3.5Asymptotictotalgeodesyandapplications4Measure-preservingalgebraiccorrespondencesonirreducibleboundedsymmetricdomains4.1Statementsofresults4.2Extensionresultsonstrictlypseudoconvexalgebraichypersurfaces4.3Alexander-typeextensionresultsinthehigher-rankcase4.4Totalgeodesyofgermsofmeasure-preservingholomorphie
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