Table Of ContentSpringer 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
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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
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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
