Complex Geometry and Dynamics: The Abel Symposium 2013 PDF
Preview Complex Geometry and Dynamics: The Abel Symposium 2013
Abel Symposia 10 John Erik Fornæss Marius Irgens Erlend Fornæss Wold Editors Complex Geometry and Dynamics The Abel Symposium 2013 ABEL SYMPOSIA Edited by the Norwegian Mathematical Society Moreinformationaboutthisseriesathttp://www.springer.com/series/7462 John Erik Fornæss (cid:129) Marius Irgens (cid:129) Erlend Fornæss Wold Editors Complex Geometry and Dynamics The Abel Symposium 2013 123 Editors JohnErikFornæss MariusIrgens DepartmentofMathematicalSciences DepartmentofMathematicalSciences NTNUGløshaugen NTNUGløshaugen Trondheim,Norway Trondheim,Norway ErlendFornæssWold DepartmentofMathematics UniversityofOslo Oslo,Norway ISSN2193-2808 ISSN2197-8549 (electronic) AbelSymposia ISBN978-3-319-20336-2 ISBN978-3-319-20337-9 (eBook) DOI10.1007/978-3-319-20337-9 LibraryofCongressControlNumber:2015955146 Mathematics Subject Classification (2010): 32H04, 37F99, 32W05, 32D15, 53C42, 32H02, 53A10, 32B15, 14H15, 32G15, 37J35, 58A15, 32V40, 32Q45, 32V35, 14J70, 14F10, 12H05, 53A20, 32V25, 32S25, 32T15, 32A07, 32H50, 37F45, 11J97, 14J10, 32U05, 32V10,32V30 SpringerChamHeidelbergNewYorkDordrechtLondon ©SpringerInternationalPublishingSwitzerland2015 Thisworkissubjecttocopyright.AllrightsarereservedbythePublisher,whetherthewholeorpartof thematerialisconcerned,specificallytherightsoftranslation,reprinting,reuseofillustrations,recitation, broadcasting,reproductiononmicrofilmsorinanyotherphysicalway,andtransmissionorinformation storageandretrieval,electronicadaptation,computersoftware,orbysimilarordissimilarmethodology nowknownorhereafterdeveloped. Theuseofgeneraldescriptivenames,registerednames,trademarks,servicemarks,etc.inthispublication doesnotimply,evenintheabsenceofaspecificstatement,thatsuchnamesareexemptfromtherelevant protectivelawsandregulationsandthereforefreeforgeneraluse. Thepublisher,theauthorsandtheeditorsaresafetoassumethattheadviceandinformationinthisbook arebelievedtobetrueandaccurateatthedateofpublication.Neitherthepublishernortheauthorsor theeditorsgiveawarranty,expressorimplied,withrespecttothematerialcontainedhereinorforany errorsoromissionsthatmayhavebeenmade. Printedonacid-freepaper Springer International Publishing AG Switzerland is part of Springer Science+Business Media (www.springer.com) Foreword TheNorwegiangovernmentestablishedtheAbelPrizeinmathematicsin2002,and the first prize was awarded in 2003. In addition to honoring the great Norwegian mathematicianNielsHenrikAbelbyawardinganinternationalprizeforoutstanding scientificworkinthefieldofmathematics,theprizeshallcontributetowardraising the status of mathematics in society and stimulate the interest for science among schoolchildrenandstudents.Inkeepingwiththisobjective,theNielsHenrikAbel Board has decided to finance annual Abel Symposia. The topic of the Symposia maybeselectedbroadlyintheareaofpureandappliedmathematics.TheSymposia should be at the highest international level and serve to build bridges between thenationalandinternationalresearchcommunities.TheNorwegianMathematical Societyisresponsiblefortheevents.Ithasalsobeendecidedthatthecontributions fromthese Symposiashouldbe presentedina seriesofproceedings,andSpringer Verlag has enthusiastically agreed to publish the series. The Niels Henrik Abel Boardisconfidentthattheserieswillbeavaluablecontributiontothemathematical literature. HelgeHolden ChairoftheNielsHenrikAbelBoard Trondheim,Norway v Preface Thetheme ofthe AbelSymposium2013was Complex Geometry,andit was held at the Norwegian University of Science and Technology, Trondheim, during July 2–5.Theeventattracted43participantsandfeaturedpresentationsby22speakers. ThescientificagendaprimarilyfocusedongeometricproblemsinSeveralComplex Variables and Complex Dynamics, including holomorphic laminations/foliations, the@-equation,CR-geometry,pluripotentialtheory,andfunctiontheory.Theaimof theAbelSymposiumwastopresentthestateoftheartonthesetopicsandtodiscuss futureresearchdirections.Thespeakersandtitleswere: 1. Bedford,E.Automorphismsofblowupsofprojectivespace 2. Berndtsson,B.TheopennessproblemandcomplexBrunn-Minkowskiinequali- ties 3. Błocki,Z.Hörmander’s@-estimate,somegeneralizationsandnewapplications 4. Demailly,J.-P.Onthecohomologyofpseudoeffectivelinebundles 5. Dihn,T.-C.Positiveclosed.p;p/-currentsandapplicationsincomplexdynam- ics 6. Ebenfelt,P.PartialrigidityofdegenerateCR-embeddingsintospheres 7. Fornstnericˇ,F.ComplexanalysisandtheCalabi-Yauproblem 8. Grushevsky,S. Meromorphic differentialswith realperiodsandthe geometry ofthemodulispaceofRiemannsurfaces 9. Huang, X. Analyticity of the local hull of holomorphy for a codimension two real-submanifoldinCn 10. Kohn,J.WeaklypseudoconvexCRmanifolds 11. McMullen,C.Entropyanddynamicsoncomplexsurfaces 12. Merker,J.Siu-YeungholomorphicsectionsofSymmT(cid:2) X 13. Mok, N. On the Zariski closure of an infinite number of totally geodesic subvarietesof˝=(cid:2) 14. Nemirovski,S.Topologyandseveralcomplexvariables 15. Ohsawa,T.LeviflatsinHopfsurfaces 16. Sibony,N.DynamicsoffoliationsbyRiemannsurfaces 17. Stensønes,B.Realanalyticdomainsandplurisubharmonicfunctions 18. Ueda,T.Semi-parabolicfixedpointsandtheirbifurcationsincomplexdimen- sion2 19. Yau,S.-T.Periodintegrals,countingcurves,andmirrorsymmetry vii viii Preface 20. Yau, S. Nonconstant CR morphisms between compact strongly pseudoconvex CRmanifoldsandetalecoveringbetweenresolutionsofisolatedsingularities 21. Yeung,S.-K.Complexhyperbolicityonthemoduliofsomehigher-dimensional manifolds 22. Zhou,X.SomeresultsonL2-extensionproblemwithoptimalestimate ThescientificcommitteeconsistedofJohnErikFornæss(NTNU),MariusIrgens (NTNU), Yum-Tong Siu (Harvard), Erlend F. Wold (Oslo), and Shing-Tung Yau (Harvard). During the symposium, a dinner was held in honor of Yum-Tong Siu’s 70th birthday.Wewouldliketodedicatetheseproceedingstohim. Theparticipantsatthesymposiumwere: EricBedford NgaimingMok BoBerndtsson StefanNemirovski ZbigniewBłocki TakeoOhsawa FushengDeng TronOmland Jean-PierreDemailly MariusOverholt KlasDiederich NilsØvrelid Tien-CuongDinh AlexanderRashkovskii PeterEbenfelt NessimSibony JohnErikFornæss Yum-TongSiu FrancForstnericˇ BeritStensønes DustyGrundmeier ShenghaoSun SamuelGrushevsky TetsuoUeda KariHag ErlendF.Wold PerHag SonyauXie Siri-MalénHøynes GuowuYao XiaojunHuang Shing-TungYau MariusIrgens StephenS.T.Yau JosephKohn Sai-KeeYeung ErikLøw Jian-HuaZheng BenediktMagnusson Xiang-YuZhou CurtisMcMullen MinxianZhu JoëlMerker WewouldliketothanktheNorwegianMathematicalSocietyandtheNilsHenrik Abel Memorial Fund for giving us the opportunity to host the Abel Symposium. We would also like to thank the administration at NTNU for their great help with the organizingand Ruth Allewelt at Springerfor her helpwith preparingthe proceedings. Trondheim,Norway JohnErikFornæss Trondheim,Norway MariusIrgens Oslo,Norway ErlendFornæssWold May15,2015 Contents PseudoautomorphismswithInvariantCurves................................ 1 EricBedford,JefferyDiller,andKyoungheeKim 1 FromCuspidalCurves... ..................................................... 6 2 ...ToBasicCremonaMaps... ............................................... 8 3 ...ToPseudoautomorphisms... .............................................. 12 4 ...ToFormulas................................................................ 14 5 TheConnectionwithCoxeterGroups........................................ 20 6 PseudoautomorphismsonMultiprojectiveSpaces........................... 22 References......................................................................... 26 TheOpennessConjectureandComplexBrunn-Minkowski Inequalities........................................................................ 29 BoBerndtsson 1 Introduction.................................................................... 29 2 TheBrunn-MinkowskiTheorem ............................................. 30 3 AComplexVariantoftheBrunn-MinkowskiTheorem..................... 31 4 TheOpennessProblem........................................................ 35 5 AConjecturalPictureforStrongOpenness.................................. 41 References......................................................................... 43 Estimatesfor@N andOptimalConstants ....................................... 45 ZbigniewBłocki 1 Introduction.................................................................... 45 2 Estimatesfor@N................................................................. 46 3 OptimalConstants............................................................. 48 References......................................................................... 50 OntheCohomologyofPseudoeffectiveLineBundles........................ 51 Jean-PierreDemailly 1 IntroductionandStatementoftheMainResults............................. 51 2 ApproximationofpshFunctionsandofClosed(1,1)-Currents............. 57 ix
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