Algebraic and Complex Geometry: In Honour of Klaus Hulek's 60th Birthday PDF
Preview Algebraic and Complex Geometry: In Honour of Klaus Hulek's 60th Birthday
Springer Proceedings in Mathematics & Statistics Anne Frühbis-Krüger Remke Nanne Kloosterman Matthias Schütt E ditors Algebraic and Complex Geometry Springer Proceedings in Mathematics & Statistics Volume 71 Forfurthervolumes: http://www.springer.com/series/10533 SpringerProceedingsinMathematics&Statistics This book series features volumes composed of selected contributions from workshops and conferences in all areas of current research in mathematics and statistics, including OR and optimization. In addition to an overall evaluation of the interest, scientific quality, and timeliness of each proposal at the hands of the publisher,individualcontributionsare allrefereedto the high qualitystandardsof leadingjournalsinthefield.Thus,thisseriesprovidestheresearchcommunitywith well-edited, authoritative reports on developments in the most exciting areas of mathematicalandstatisticalresearchtoday. Anne FruRhbis-KruRger • Remke Nanne Kloosterman • Matthias SchuRtt Editors Algebraic and Complex Geometry In Honour of Klaus Hulek’s 60th Birthday 123 Editors AnneFruRhbis-KruRger RemkeNanneKloosterman LeibnizUniversitätHannover Humboldt-UniversityBerlin Hannover,Germany Berlin,Germany MatthiasSchuRtt LeibnizUniversitätHannover Hannover,Germany ISSN2194-1009 ISSN2194-1017(electronic) ISBN978-3-319-05403-2 ISBN978-3-319-05404-9(eBook) DOI10.1007/978-3-319-05404-9 SpringerChamHeidelbergNewYorkDordrechtLondon LibraryofCongressControlNumber:2014950053 MathematicsSubjectClassification(2010):14J10,14E30,14J28,14J32,14J50,14T05 ©SpringerInternationalPublishingSwitzerland2014 Thisworkissubjecttocopyright.AllrightsarereservedbythePublisher,whetherthewholeorpartof thematerialisconcerned,specificallytherightsoftranslation,reprinting,reuseofillustrations,recitation, broadcasting,reproductiononmicrofilmsorinanyotherphysicalway,andtransmissionorinformation storageandretrieval,electronicadaptation,computersoftware,orbysimilarordissimilarmethodology nowknownorhereafterdeveloped.Exemptedfromthislegalreservationarebriefexcerptsinconnection with reviews or scholarly analysis or material supplied specifically for the purpose of being entered and executed on a computer system, for exclusive use by the purchaser of the work. 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Printedonacid-freepaper SpringerispartofSpringerScience+BusinessMedia(www.springer.com) Preface ThisvolumeofPROMSgrewoutoftheinternationalconferenceon“Algebraicand ComplexGeometry”,whichtookplaceatLeibnizUniversitätHannoverduringthe weekofSeptember10through14,2012.Theeventwasorganisedontheoccasion ofKlausHulek’s60thbirthday;itiswithgreatpleasurethatwededicatethisvolume tohim. We would like to thank the members of the Scientific Advisory Board of the conference,DavidEisenbud,NigelHitchinandThomasPeternell,fortheircrucial inputinsettinguptheprogram.Theconferencewouldhavebeenimpossiblewithout thegeneroussupportfromthefollowinginstitutions: • DeutscheForschungsgemeinschaft • MWKNiedersachsen • FoundationCompositio • GRK1463“Analysis,GeometryandStringTheory” • ManyotherinstitutionsatLeibnizUniversitätHannover Especially, we would like to express our gratitude to all members of the Institute of Algebraic Geometry at LUH for all the helping hands before and during the conference,inparticulartooursecretariesNicoleRottländerandSimoneReimann. Ourthanksgotoalltheauthorscontributingtothisvolume,andtothereferees forthethoroughjobtheyhavedone.MatthiasFreisetookcareofthecompilationof thisvolume,andwethankhimverymuch. Hannover,Germany AnneFrühbis-Krüger Berlin,Germany RemkeKloosterman Hannover,Germany MatthiasSchütt v Contents StabilityConditionsandPositivityofInvariantsofFibrations............. 1 M.A.BarjaandL.Stoppino OntheSecondLowerQuotientoftheFundamentalGroup ................ 41 ArnaudBeauville McKayCorrespondenceoverNonAlgebraicallyClosedFields ............ 47 MarkBlume GonalityofAlgebraicCurvesandGraphs.................................... 77 LuciaCaporaso CausticsofPlaneCurves,TheirBirationalityandMatrixProjections.... 109 FabrizioCatanese LimitsofPluri–TangentPlanestoQuarticSurfaces......................... 123 CiroCilibertoandThomasDedieu OnImagesofWeakFanoManifoldsII........................................ 201 OsamuFujinoandYoshinoriGongyo TheHyperholomorphicLineBundle .......................................... 209 NigelHitchin HodgeNumbersfortheCohomologyofCalabi-YauTypeLocal Systems............................................................................ 225 HenningHollbornandStefanMüller–Stach LagrangianFibrationsofHolomorphic-SymplecticVarieties ofK3Œn(cid:2)-Type...................................................................... 241 EyalMarkman vii viii Contents ContactKählerManifolds:SymmetriesandDeformations................. 285 ThomasPeternellandFlorianSchrack ListofParticipants............................................................... 309 CompleteListofTalks........................................................... 313 Introduction The following paragraphs are meant to give a brief outline of the topics of the conference “Algebraic and Complex Geometry” and the content of this PROMS volume.Algebraicandcomplexgeometryareexceptionallyactiveareasofresearch in pure mathematics which have seen many novel developments in recent years, influencing numerous other areas such as differential geometry, number theory, representationtheory,andmathematicalphysics.Manyoftheseinterestingaspects willbereflectedinwhatfollows. 1 Topicofthe Conference Theprogramoftheconferencewasdesignedtoreviewthelatestachievementsand innovationsin algebraicandcomplexgeometry.Theprogramfeatured23lectures fromvarioussubfields,allowingabroadscope,butputtingspecificemphasisontwo subjectsofspectacularrecentandongoingprogress:geometryofmodulispacesand irreduciblesymplecticmanifolds(Hyperkählermanifolds). GeometryofModuliSpaces Moduli spaces are a key object of study in algebraic and complex geometry. OriginallyintroducedbyRiemannin thecase ofcurves,modulispacesturnedout tobeinterestingbothfortheirownsakeandforthenumerousimplicationstoother fieldssuch as e.g.numbertheory(arithmeticgeometry)andmathematicalphysics (stringtheory). Recently, there has been a particular interest in establishing the geometric and topologicalpropertiesofmodulispaces.Inparticular,newlydevelopedtechniques yield results on the Kodaira dimension and on the cohomologyof several moduli ix
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