Recent Advances in Algebraic Geometry: A Volume in Honor of Rob Lazarsfeld’s 60th Birthday

451 Pages·2015·8.037 MB·English

by  Christopher D. Hacon, Mircea Mustaţă, Mihnea Popa (eds.)

LONDONMATHEMATICALSOCIETYLECTURENOTESERIES
ManagingEditor:ProfessorM.Reid,MathematicsInstitute,
UniversityofWarwick,CoventryCV47AL,UnitedKingdom
Thetitlesbelowareavailablefrombooksellers,orfromCambridgeUniversityPressat
http://www.cambridge.org/mathematics
287 TopicsonRiemannsurfacesandFuchsiangroups,E.BUJALANCE,A.F.COSTA&E.MARTÍNEZ(eds)
288 Surveysincombinatorics,2001,J.W.P.HIRSCHFELD(ed)
289 AspectsofSobolev-typeinequalities,L.SALOFF-COSTE
290 QuantumgroupsandLietheory,A.PRESSLEY(ed)
291 Titsbuildingsandthemodeltheoryofgroups,K.TENT(ed)
292 Aquantumgroupsprimer,S.MAJID
293 SecondorderpartialdifferentialequationsinHilbertspaces,G.DAPRATO&J.ZABCZYK
294 Introductiontooperatorspacetheory,G.PISIER
295 Geometryandintegrability,L.MASON&Y.NUTKU(eds)
296 Lecturesoninvarianttheory,I.DOLGACHEV
297 Thehomotopycategoryofsimplyconnected4-manifolds,H.-J.BAUES
298 Higheroperads,highercategories,T.LEINSTER(ed)
299 Kleiniangroupsandhyperbolic3-manifolds,Y.KOMORI,V.MARKOVIC&C.SERIES(eds)
300 IntroductiontoMöbiusdifferentialgeometry,U.HERTRICH-JEROMIN
301 StablemodulesandtheD(2)-problem,F.E.A.JOHNSON
302 DiscreteandcontinuousnonlinearSchrödingersystems,M.J.ABLOWITZ,B.PRINARI&A.D.TRUBATCH
303 Numbertheoryandalgebraicgeometry,M.REID&A.SKOROBOGATOV(eds)
304 GroupsStAndrews2001inOxfordI,C.M.CAMPBELL,E.F.ROBERTSON&G.C.SMITH(eds)
305 GroupsStAndrews2001inOxfordII,C.M.CAMPBELL,E.F.ROBERTSON&G.C.SMITH(eds)
306 Geometricmechanicsandsymmetry,J.MONTALDI&T.RATIU(eds)
307 Surveysincombinatorics2003,C.D.WENSLEY(ed.)
308 Topology,geometryandquantumfieldtheory,U.L.TILLMANN(ed)
309 Coringsandcomodules,T.BRZEZINSKI&R.WISBAUER
310 Topicsindynamicsandergodictheory,S.BEZUGLYI&S.KOLYADA(eds)
311 Groups:topological,combinatorialandarithmeticaspects,T.W.MÜLLER(ed)
312 Foundationsofcomputationalmathematics,Minneapolis2002,F.CUCKERetal(eds)
313 Transcendentalaspectsofalgebraiccycles,S.MÜLLER-STACH&C.PETERS(eds)
314 Spectralgeneralizationsoflinegraphs,D.CVETKOVIC,P.ROWLINSON&S.SIMIC
315 Structuredringspectra,A.BAKER&B.RICHTER(eds)
316 Linearlogicincomputerscience,T.EHRHARD,P.RUET,J.-Y.GIRARD&P.SCOTT(eds)
317 Advancesinellipticcurvecryptography,I.F.BLAKE,G.SEROUSSI&N.P.SMART(eds)
318 Perturbationoftheboundaryinboundary-valueproblemsofpartialdifferentialequations,D.HENRY
319 DoubleaffineHeckealgebras,I.CHEREDNIK
320 L-functionsandGaloisrepresentations,D.BURNS,K.BUZZARD&J.NEKOVÁR(eds)
321 Surveysinmodernmathematics,V.PRASOLOV&Y.ILYASHENKO(eds)
322 Recentperspectivesinrandommatrixtheoryandnumbertheory,F.MEZZADRI&N.C.SNAITH(eds)
323 Poissongeometry,deformationquantisationandgrouprepresentations,S.GUTTetal(eds)
324 Singularitiesandcomputeralgebra,C.LOSSEN&G.PFISTER(eds)
325 LecturesontheRicciflow,P.TOPPING
326 ModularrepresentationsoffinitegroupsofLietype,J.E.HUMPHREYS
327 Surveysincombinatorics2005,B.S.WEBB(ed)
328 Fundamentalsofhyperbolicmanifolds,R.CANARY,D.EPSTEIN&A.MARDEN(eds)
329 SpacesofKleiniangroups,Y.MINSKY,M.SAKUMA&C.SERIES(eds)
330 Noncommutativelocalizationinalgebraandtopology,A.RANICKI(ed)
331 Foundationsofcomputationalmathematics,Santander2005,L.MPARDO,A.PINKUS,E.SÜLI&
M.J.TODD(eds)
332 Handbookoftiltingtheory,L.ANGELERIHÜGEL,D.HAPPEL&H.KRAUSE(eds)
333 Syntheticdifferentialgeometry(2ndEdition),A.KOCK
334 TheNavier–Stokesequations,N.RILEY&P.DRAZIN
335 Lecturesonthecombinatoricsoffreeprobability,A.NICA&R.SPEICHER
336 Integralclosureofideals,rings,andmodules,I.SWANSON&C.HUNEKE
337 MethodsinBanachspacetheory,J.M.F.CASTILLO&W.B.JOHNSON(eds)
338 Surveysingeometryandnumbertheory,N.YOUNG(ed)
339 GroupsStAndrews2005I,C.M.CAMPBELL,M.R.QUICK,E.F.ROBERTSON&G.C.SMITH(eds)
340 GroupsStAndrews2005II,C.M.CAMPBELL,M.R.QUICK,E.F.ROBERTSON&G.C.SMITH(eds)
341 Ranksofellipticcurvesandrandommatrixtheory,J.B.CONREY,D.W.FARMER,F.MEZZADRI&
N.C.SNAITH(eds)
342 Ellipticcohomology,H.R.MILLER&D.C.RAVENEL(eds)
343 AlgebraiccyclesandmotivesI,J.NAGEL&C.PETERS(eds)
344 AlgebraiccyclesandmotivesII,J.NAGEL&C.PETERS(eds)
345 Algebraicandanalyticgeometry,A.NEEMAN
346 Surveysincombinatorics2007,A.HILTON&J.TALBOT(eds)
347 Surveysincontemporarymathematics,N.YOUNG&Y.CHOI(eds)
348 Transcendentaldynamicsandcomplexanalysis,P.J.RIPPON&G.M.STALLARD(eds)
349 ModeltheorywithapplicationstoalgebraandanalysisI,Z.CHATZIDAKIS,D.MACPHERSON,A.PILLAY&
A.WILKIE(eds)
350 ModeltheorywithapplicationstoalgebraandanalysisII,Z.CHATZIDAKIS,D.MACPHERSON,A.PILLAY&
A.WILKIE(eds)
351 FinitevonNeumannalgebrasandmasas,A.M.SINCLAIR&R.R.SMITH
352 Numbertheoryandpolynomials,J.MCKEE&C.SMYTH(eds)
353 Trendsinstochasticanalysis,J.BLATH,P.MÖRTERS&M.SCHEUTZOW(eds)
354 Groupsandanalysis,K.TENT(ed)
355 Non-equilibriumstatisticalmechanicsandturbulence,J.CARDY,G.FALKOVICH&K.GAWEDZKI
356 EllipticcurvesandbigGaloisrepresentations,D.DELBOURGO
357 Algebraictheoryofdifferentialequations,M.A.H.MACCALLUM&A.V.MIKHAILOV(eds)
358 Geometricandcohomologicalmethodsingrouptheory,M.R.BRIDSON,P.H.KROPHOLLER&
I.J.LEARY(eds)
359 Modulispacesandvectorbundles,L.BRAMBILA-PAZ,S.B.BRADLOW,O.GARCÍA-PRADA&
S.RAMANAN(eds)
360 Zariskigeometries,B.ZILBER
361 Words:Notesonverbalwidthingroups,D.SEGAL
362 Differentialtensoralgebrasandtheirmodulecategories,R.BAUTISTA,L.SALMERÓN&R.ZUAZUA
363 Foundationsofcomputationalmathematics,HongKong2008,F.CUCKER,A.PINKUS&M.J.TODD(eds)
364 Partialdifferentialequationsandfluidmechanics,J.C.ROBINSON&J.L.RODRIGO(eds)
365 Surveysincombinatorics2009,S.HUCZYNSKA,J.D.MITCHELL&C.M.RONEY-DOUGAL(eds)
366 Highlyoscillatoryproblems,B.ENGQUIST,A.FOKAS,E.HAIRER&A.ISERLES(eds)
367 Randommatrices:Highdimensionalphenomena,G.BLOWER
368 GeometryofRiemannsurfaces,F.P.GARDINER,G.GONZÁLEZ-DIEZ&C.KOUROUNIOTIS(eds)
369 Epidemicsandrumoursincomplexnetworks,M.DRAIEF&L.MASSOULIÉ
370 Theoryofp-adicdistributions,S.ALBEVERIO,A.YU.KHRENNIKOV&V.M.SHELKOVICH
371 Conformalfractals,F.PRZYTYCKI&M.URBANSKI
372 Moonshine:Thefirstquartercenturyandbeyond,J.LEPOWSKY,J.MCKAY&M.P.TUITE(eds)
373 Smoothness,regularityandcompleteintersection,J.MAJADAS&A.G.RODICIO
374 Geometricanalysisofhyperbolicdifferentialequations:Anintroduction,S.ALINHAC
375 Triangulatedcategories,T.HOLM,P.JØRGENSEN&R.ROUQUIER(eds)
376 Permutationpatterns,S.LINTON,N.RUŠKUC&V.VATTER(eds)
377 AnintroductiontoGaloiscohomologyanditsapplications,G.BERHUY
378 Probabilityandmathematicalgenetics,N.H.BINGHAM&C.M.GOLDIE(eds)
379 Finiteandalgorithmicmodeltheory,J.ESPARZA,C.MICHAUX&C.STEINHORN(eds)
380 Realandcomplexsingularities,M.MANOEL,M.C.ROMEROFUSTER&C.T.CWALL(eds)
381 Symmetriesandintegrabilityofdifferenceequations,D.LEVI,P.OLVER,Z.THOMOVA&
P.WINTERNITZ(eds)
382 Forcingwithrandomvariablesandproofcomplexity,J.KRAJÍCˇEK
383 Motivicintegrationanditsinteractionswithmodeltheoryandnon-ArchimedeangeometryI,R.CLUCKERS,
J.NICAISE&J.SEBAG(eds)
384 Motivicintegrationanditsinteractionswithmodeltheoryandnon-ArchimedeangeometryII,R.CLUCKERS,
J.NICAISE&J.SEBAG(eds)
385 EntropyofhiddenMarkovprocessesandconnectionstodynamicalsystems,B.MARCUS,K.PETERSEN&
T.WEISSMAN(eds)
386 Independence-friendlylogic,A.L.MANN,G.SANDU&M.SEVENSTER
387 GroupsStAndrews2009inBathI,C.M.CAMPBELLetal(eds)
388 GroupsStAndrews2009inBathII,C.M.CAMPBELLetal(eds)
389 Randomfieldsonthesphere,D.MARINUCCI&G.PECCATI
390 Localizationinperiodicpotentials,D.E.PELINOVSKY
391 Fusionsystemsinalgebraandtopology,M.ASCHBACHER,R.KESSAR&B.OLIVER
392 Surveysincombinatorics2011,R.CHAPMAN(ed)
393 Non-abelianfundamentalgroupsandIwasawatheory,J.COATESetal(eds)
394 Variationalproblemsindifferentialgeometry,R.BIELAWSKI,K.HOUSTON&M.SPEIGHT(eds)
395 Howgroupsgrow,A.MANN
396 Arithmeticdfferentialoperatorsoverthep-adicIntegers,C.C.RALPH&S.R.SIMANCA
397 HyperbolicgeometryandapplicationsinquantumChaosandcosmology,J.BOLTE&F.STEINER(eds)
398 Mathematicalmodelsincontactmechanics,M.SOFONEA&A.MATEI
399 Circuitdoublecoverofgraphs,C.-Q.ZHANG
400 Densespherepackings:ablueprintforformalproofs,T.HALES
401 AdoubleHallalgebraapproachtoaffinequantumSchur-Weyltheory,B.DENG,J.DU&Q.FU
402 Mathematicalaspectsoffluidmechanics,J.ROBINSON,J.L.RODRIGO&W.SADOWSKI(eds)
403 Foundationsofcomputationalmathematics:Budapest2011,F.CUCKER,T.KRICK,A.SZANTO&
A.PINKUS(eds)
404 Operatormethodsforboundaryvalueproblems,S.HASSI,H.S.V.DESNOO&F.H.SZAFRANIEC(eds)
405 Torsors,étalehomotopyandapplicationstorationalpoints,A.N.SKOROBOGATOV(ed)
406 Appalachiansettheory,J.CUMMINGS&E.SCHIMMERLING(eds)
407 Themaximalsubgroupsofthelow-dimensionalfiniteclassicalgroups,J.N.BRAY,D.F.HOLT&
C.M.RONEY-DOUGAL
408 Complexityscience:theWarwickmaster’scourse,R.BALL,R.S.MACKAY&V.KOLOKOLTSOV(eds)
409 Surveysincombinatorics2013,S.BLACKBURN,S.GERKE&M.WILDON(eds)
410 Representationtheoryandharmonicanalysisofwreathproductsoffinitegroups,
T.CECCHERINI-SILBERSTEIN,F.SCARABOTTI&F.TOLLI
411 Modulispaces,L.BRAMBILA-PAZ,O.GARCÍA-PRADA,P.NEWSTEAD&R.P.THOMAS(eds)
412 Automorphismsandequivalencerelationsintopologicaldynamics,D.B.ELLIS&R.ELLIS
413 Optimaltransportation,Y.OLLIVIER,H.PAJOT&C.VILLANI(eds)
414 AutomorphicformsandGaloisrepresentationsI,F.DIAMOND,P.KASSAEI&M.KIM(eds)
415 AutomorphicformsandGaloisrepresentationsII,F.DIAMOND,P.KASSAEI&M.KIM(eds)
LondonMathematicalSocietyLectureNoteSeries:417
Recent Advances in Algebraic Geometry
A Volume in Honor of Rob Lazarsfeld’s
60th Birthday
Editedby
CHRISTOPHER D. HACON
UniversityofUtah
MIRCEA MUSTAT¸A˘
UniversityofMichigan
MIHNEA POPA
NorthwesternUniversity
UniversityPrintingHouse,CambridgeCB28BS,UnitedKingdom
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(cid:2)c CambridgeUniversityPress2015
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Contents
Listofcontributors pagevii
Preface xi
1 Theeffectofpointsfatteningindimensionthree 1
Th.BauerandT.Szemberg
2 Someremarksonsurfacemodulianddeterminants 13
A.Bertram
3 Valuationspacesandmultiplieridealsonsingularvarieties 29
S.Boucksom,T.deFernex,C.Favre,
andS.Urbinati
4 Linearrangementsmodelingcurvesofhighdegree:Equations,
syzygies,andsecants 52
G.Burnham,Z.Rosen,J.Sidman,andP.Vermeire
5 RationallyconnectedmanifoldsandsemipositivityoftheRicci
curvature 71
F.Campana,J.-P.Demailly,andTh.Peternell
6 SubcanonicalgradedringswhicharenotCohen–Macaulay 92
F.Catanese(withanAppendixbyJ.Wahl)
7 ThreefolddivisorialcontractionstosingularitiesofcEtype 102
J.A.Chen
8 SpecialprimeFanofourfoldsofdegree10andindex2 123
O.Debarre,A.Iliev,andL.Manivel
9 Configurationspacesofcomplexandrealspheres 156
I.DolgachevandB.Howard
vi Contents
10 TwentypointsinP3 180
D.Eisenbud,R.Hartshorne,andF.-O.Schreyer
11 TheBettitableofahigh-degreecurveisasymptoticallypure 200
D.Erman
12 Partial positivity: Geometry and cohomology of q-ample line
bundles 207
D.GrebandA.Küronya
13 Genericvanishingfailsforsingularvarietiesandin
characteristic p>0 240
C.D.HaconandS.J.Kovács
14 DeformationsofellipticCalabi–Yaumanifolds 254
J.Kollár
15 Derivedequivalenceandnon-vanishinglociII 291
L.LombardiandM.Popa
16 The automorphism groups of Enriques surfaces covered by
symmetricquarticsurfaces 307
S.MukaiandH.Ohashi
17 Lower-order asymptotics for Szegö and Toeplitz kernels under
Hamiltoniancircleactions 321
R.Paoletti
18 GaussianmapsandgenericvanishingI:Subvarietiesofabelian
varieties 370
G.Pareschi
19 Torsion points on cohomology support loci: From D-modules
toSimpson’stheorem 405
C.Schnell
20 Rationalequivalenceof0-cyclesonK3surfacesandconjectures
ofHuybrechtsandO’Grady 422
C.Voisin
Contributors
Thomas Bauer Fachbereich Mathematik und Informatik, Philipps-Univer-
sität Marburg, Hans-Meerwein-Straße, D-35032 Marburg, Germany;
[email protected]
Aaron Bertram Department of Mathematics, University of Utah, Salt Lake
City,UT84112-0090,USA;[email protected]
Sébastien BoucksomCNRS-InstitutdeMathématiquesdeJussieu,4place
Jussieu,75252ParisCedex,France;[email protected]
Gregory Burnham c/o Bridgewater Associates, 1 Glendinning plane, West-
port,CT06880,USA
Frédéric Campana Université de Lorraine, Institut Élie Cartan, UMR
7502 du CNRS, BP 70239, 54506 Vandœuvre-lès-Nancy Cedex, France;
[email protected]
Fabrizio Catanese Lehrstuhl Mathematik VIII, Mathematisches Institut
der Universität Bayreuth, NW II, Universitätsstr. 30, 95447 Bayreuth,
Germany;[email protected]
JungkaiAlfredChen NationalCenterforTheoreticalSciences,TaipeiOffice
andDepartmentofMathematics,NationalTaiwanUniversity,Taipei106,
Taiwan;[email protected]
Olivier Debarre Département de Mathématiques et Applications, École
Normale Supérieure et CNRS, 45 rue d’Ulm, 75230 Paris cedex 05,
France;[email protected]
Tommaso de Fernex Department of Mathematics, University of Utah, Salt
LakeCity,UT48112-0090,USA;[email protected]
Jean-Pierre Demailly Université de Grenoble I, Institut Fourier, UMR
5582 du CNRS, BP 74, 38402 Saint-Martin d’Hères, France;
[email protected]
IgorDolgachev DepartmentofMathematics,UniversityofMichigan,525E.
UniversityAve.,AnnArbor,MI49109,USA;[email protected]
viii Listofcontributors
David Eisenbud Department of Mathematics, University of California,
Berkeley,Berkeley,CA94720;[email protected]
Daniel Erman Department of Mathematics, University of Wisconsin, Madi-
son,WI53706,USA;[email protected]
Charles Favre CNRS - Centre de Mathématiques Laurent Schwartz, École
Polytechnique,91128PalaiseauCedex,France;
[email protected]
Daniel Greb Ruhr-Universität Bochum, Fakultät für Mathematik, Arbeits-
gruppeAlgebra/Topologie,44780Bochum,Germany;
[email protected]
Christopher D. Hacon Department of Mathematics, University of Utah,
155 South 1400 East, Salt Lake City, UT 48112-0090, USA;
[email protected]
Robin Hartshorne Department of Mathematics, University of California,
Berkeley,Berkeley,CA94720;[email protected]
Benjamin Howard Center for Communications Research, Institute for
Defense Analysis, 805 Bunn Drive, Princeton, NJ 08540, USA;
[email protected]
Atanas Iliev Department of Mathematics, Seoul National University,
GwanakCampus,Bldg.27,Seoul151-747,Korea;
[email protected]
János Kollár Department of Mathematics, Princeton University, Princeton,
NJ08544-1000,USA;[email protected]
SándorJKovács UniversityofWashington,DepartmentofMathematics,Box
354350,Seattle,WA98195-4350,USA;[email protected]
AlexKüronya BudapestUniversityofTechnologyandEconomics,Department
of Algebra. Address: Albert-Ludwigs-Universität Freiburg, Mathematis-
chesInstitut,Eckerstraße1,D-79104Freiburg,Germany;
[email protected]
Luigi Lombardi Mathematisches Institut, Universität Bonn, Endenicher
Allee60,Bonn53115,Germany;[email protected]
LaurentManivel InstitutFourier,UniversitédeGrenobleIetCNRS,BP74,
38402Saint-Martind’Hères,France;
[email protected]
ShigeruMukai ResearchInstituteforMathematicalSciences,KyotoUniver-
sity,Kyoto606-8502,Japan;[email protected]
Hisanori Ohashi Department of Mathematics, Faculty of Science and Tech-
nology, Tokyo University of Science, 2641 Yamazaki, Noda, Chiba 278-
8510,Japan;[email protected],
[email protected]
Listofcontributors ix
Roberto Paoletti Dipartimento di Matematica e Applicazioni, Università
degli Studi di Milano Bicocca, Via R. Cozzi 53, 20125 Milano, Italy;
[email protected]
GiuseppePareschi DipartimentodiMatematica,UniversitàdiRoma,
TorVergata,VialedellaRicercaScientifica,00133Roma,Italy;
[email protected]
Thomas Peternell Universität Bayreuth, Mathematisches Institut, D-95440
Bayreuth,Germany;[email protected]
Mihnea Popa Department of Mathematics, Northwestern University, 2033
SheridanRoad,Evanston,IL60208-2730,USA;
[email protected]
Zvi Rosen Department of Mathematics, University of California, Berkeley,
Berkeley,CA94720,USA;[email protected]
ChristianSchnell DepartmentofMathematics,StonyBrookUniversity,Stony
Brook,NY11794,USA;[email protected]
Frank-Olaf Schreyer Mathematik und Informatik, Universität des Saarlan-
des,CampusE24,D-66123Saarbrücken,Germany;
[email protected]
Jessica Sidman Department of Mathematics and Statistics, Mount Holyoke
College,SouthHadley,MA01075,USA;[email protected]
Tomasz Szemberg Instytut Matematyki UP, Podchora¸z˙ych 2, PL-30-084
Kraków,Poland;[email protected]
Stefano Urbinati Università degli Studi di Padova, Via Trieste 63, 35121
Padova,Italy;[email protected]
Peter Vermeire Department of Mathematics, Central Michigan University,
MountPleasant,MI48859,USA;[email protected]
ClaireVoisin CNRSandÉcolePolytechnique,CentredemathématiquesLau-
rentSchwartz,91128PalaiseauCédex,France;
[email protected]
Johnathan Wahl University of North Carolina at Chapel Hill, Chapel Hill,
NC27599-3250,USA;[email protected]