Facets of Algebraic Geometry: Volume 1: A Collection in Honor of William Fulton's 80th Birthday PDF
Preview Facets of Algebraic Geometry: Volume 1: A Collection in Honor of William Fulton's 80th Birthday
LONDONMATHEMATICALSOCIETYLECTURENOTESERIES ManagingEditor:ProfessorEndreSu¨li,MathematicalInstitute,UniversityofOxford, WoodstockRoad,OxfordOX26GG,UnitedKingdom Thetitlesbelowareavailablefrombooksellers,orfromCambridgeUniversityPressat www.cambridge.org/mathematics 366 Highlyoscillatoryproblems, B.ENGQUIST,A.FOKAS,E.HAIRER&A.ISERLES(eds) 367 Randommatrices:Highdimensionalphenomena, G.BLOWER 368 GeometryofRiemannsurfaces, F.P.GARDINER,G.GONZA´LEZ-DIEZ&C.KOUROUNIOTIS(eds) 369 Epidemicsandrumoursincomplexnetworks, M.DRAIEF&L.MASSOULIE´ 370 Theoryofp-adicdistributions, S.ALBEVERIO,A.YU.KHRENNIKOV&V.M.SHELKOVICH 371 Conformalfractals, F.PRZYTYCKI&M.URBAN´SKI 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.RUSˇKUC&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.KRAJ´ICˇEK 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 Arithmeticdifferentialoperatorsoverthep-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.C.ROBINSON,J.L.RODRIGO&W.SADOWSKI(eds) 403 Foundationsofcomputationalmathematics,Budapest2011, F.CUCKER,T.KRICK,A.PINKUS& A.SZANTO(eds) 404 Operatormethodsforboundaryvalueproblems, S.HASSI,H.S.V.DESNOO&F.H.SZAFRANIEC(eds) 405 Torsors,e´talehomotopyandapplicationstorationalpoints, 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,V.KOLOKOLTSOV&R.S.MACKAY(eds) 409 Surveysincombinatorics2013, S.R.BLACKBURN,S.GERKE&M.WILDON(eds) 410 Representationtheoryandharmonicanalysisofwreathproductsoffinitegroups, T.CECCHERINI-SILBERSTEIN,F.SCARABOTTI&F.TOLLI 411 Modulispaces, L.BRAMBILA-PAZ,O.GARC´IA-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.L.KASSAEI&M.KIM(eds) 415 AutomorphicformsandGaloisrepresentationsII, F.DIAMOND,P.L.KASSAEI&M.KIM(eds) 416 Reversibilityindynamicsandgrouptheory, A.G.O’FARRELL&I.SHORT 417 Recentadvancesinalgebraicgeometry, C.D.HACON,M.MUSTAT¸A˘&M.POPA(eds) 418 TheBloch–KatoconjecturefortheRiemannzetafunction, J.COATES,A.RAGHURAM,A.SAIKIA& R.SUJATHA(eds) 419 TheCauchyproblemfornon-Lipschitzsemi-linearparabolicpartialdifferentialequations, J.C.MEYER& D.J.NEEDHAM 420 Arithmeticandgeometry, L.DIEULEFAITetal(eds) 421 O-minimalityandDiophantinegeometry, G.O.JONES&A.J.WILKIE(eds) 422 GroupsStAndrews2013, C.M.CAMPBELLetal(eds) 423 Inequalitiesforgrapheigenvalues, Z.STANIC´ 424 Surveysincombinatorics2015, A.CZUMAJetal(eds) 425 Geometry,topologyanddynamicsinnegativecurvature, C.S.ARAVINDA,F.T.FARRELL& J.-F.LAFONT(eds) 426 Lecturesonthetheoryofwaterwaves, T.BRIDGES,M.GROVES&D.NICHOLLS(eds) 427 RecentadvancesinHodgetheory, M.KERR&G.PEARLSTEIN(eds) 428 GeometryinaFre´chetcontext, C.T.J.DODSON,G.GALANIS&E.VASSILIOU 429 Sheavesandfunctionsmodulop, L.TAELMAN 430 RecentprogressinthetheoryoftheEulerandNavier–Stokesequations, J.C.ROBINSON,J.L.RODRIGO, W.SADOWSKI&A.VIDAL-LO´PEZ(eds) 431 Harmonicandsubharmonicfunctiontheoryontherealhyperbolicball, M.STOLL 432 Topicsingraphautomorphismsandreconstruction(2ndEdition), J.LAURI&R.SCAPELLATO 433 RegularandirregularholonomicD-modules, M.KASHIWARA&P.SCHAPIRA 434 Analyticsemigroupsandsemilinearinitialboundaryvalueproblems(2ndEdition), K.TAIRA 435 GradedringsandgradedGrothendieckgroups, R.HAZRAT 436 Groups,graphsandrandomwalks, T.CECCHERINI-SILBERSTEIN,M.SALVATORI& E.SAVA-HUSS(eds) 437 Dynamicsandanalyticnumbertheory, D.BADZIAHIN,A.GORODNIK&N.PEYERIMHOFF(eds) 438 Randomwalksandheatkernelsongraphs, M.T.BARLOW 439 Evolutionequations, K.AMMARI&S.GERBI(eds) 440 Surveysincombinatorics2017, A.CLAESSONetal(eds) 441 Polynomialsandthemod2SteenrodalgebraI, G.WALKER&R.M.W.WOOD 442 Polynomialsandthemod2SteenrodalgebraII, G.WALKER&R.M.W.WOOD 443 Asymptoticanalysisingeneralrelativity, T.DAUDE´,D.HA¨FNER&J.-P.NICOLAS(eds) 444 Geometricandcohomologicalgrouptheory, P.H.KROPHOLLER,I.J.LEARY,C.MART´INEZ-PE´REZ& B.E.A.NUCINKIS(eds) 445 Introductiontohiddensemi-Markovmodels, J.VANDERHOEK&R.J.ELLIOTT 446 Advancesintwo-dimensionalhomotopyandcombinatorialgrouptheory, W.METZLER& S.ROSEBROCK(eds) 447 Newdirectionsinlocallycompactgroups, P.-E.CAPRACE&N.MONOD(eds) 448 Syntheticdifferentialtopology, M.C.BUNGE,F.GAGO&A.M.SANLUIS 449 Permutationgroupsandcartesiandecompositions, C.E.PRAEGER&C.SCHNEIDER 450 Partialdifferentialequationsarisingfromphysicsandgeometry, M.BENAYEDetal(eds) 451 Topologicalmethodsingrouptheory, N.BROADDUS,M.DAVIS,J.-F.LAFONT&I.ORTIZ(eds) 452 Partialdifferentialequationsinfluidmechanics, C.L.FEFFERMAN,J.C.ROBINSON& J.L.RODRIGO(eds) 453 Stochasticstabilityofdifferentialequationsinabstractspaces, K.LIU 454 Beyondhyperbolicity, M.HAGEN,R.WEBB&H.WILTON(eds) 455 GroupsStAndrews2017inBirmingham, C.M.CAMPBELLetal(eds) 456 Surveysincombinatorics2019, A.LO,R.MYCROFT,G.PERARNAU&A.TREGLOWN(eds) 457 Shimuravarieties, T.HAINES&M.HARRIS(eds) 458 IntegrablesystemsandalgebraicgeometryI, R.DONAGI&T.SHASKA(eds) 459 IntegrablesystemsandalgebraicgeometryII, R.DONAGI&T.SHASKA(eds) 460 Wigner-typetheoremsforHilbertGrassmannians, M.PANKOV 461 Analysisandgeometryongraphsandmanifolds, M.KELLER,D.LENZ&R.K.WOJCIECHOWSKI 462 ZetaandL-functionsofvarietiesandmotives, B.KAHN 463 Differentialgeometryinthelarge, O.DEARRICOTTetal(eds) 464 Lecturesonorthogonalpolynomialsandspecialfunctions, H.S.COHL&M.E.H.ISMAIL(eds) 465 ConstrainedWillmoresurfaces, A´.C.QUINTINO 466 Invarianceofmodulesunderautomorphismsoftheirenvelopesandcovers, A.K.SRIVASTAVA, A.TUGANBAEV&P.A.GUILASENSIO 467 ThegenesisoftheLanglandsprogram, J.MUELLER&F.SHAHIDI 468 (Co)endcalculus, F.LOREGIAN 469 Computationalcryptography, J.W.BOS&M.STAM(eds) 470 Surveysincombinatorics2021, K.K.DABROWSKIetal(eds) 471 Matrixanalysisandentrywisepositivitypreservers, A.KHARE 472 FacetsofalgebraicgeometryI, P.ALUFFIetal(eds) 473 FacetsofalgebraicgeometryII, P.ALUFFIetal(eds) 474 Equivarianttopologyandderivedalgebra, S.BALCHIN,D.BARNES,M.KE¸DZIOREK &M.SZYMIK(eds) 475 EffectiveresultsandmethodsforDiophantineequationsoverfinitelygenerateddomains, J.-H.EVERTSE &K.GYO˝RY LondonMathematicalSocietyLectureNoteSeries:472 Facets of Algebraic Geometry A Collection in Honor of William Fulton’s 80th Birthday volume 1 Editedby PAOLO ALUFFI FloridaStateUniversity DAVID ANDERSON OhioStateUniversity MILENA HERING UniversityofEdinburgh MIRCEA MUSTAT¸A˘ UniversityofMichigan,AnnArbor SAM PAYNE UniversityofTexas,Austin UniversityPrintingHouse,CambridgeCB28BS,UnitedKingdom OneLibertyPlaza,20thFloor,NewYork,NY10006,USA 477WilliamstownRoad,PortMelbourne,VIC3207,Australia 314–321,3rdFloor,Plot3,SplendorForum,JasolaDistrictCentre,NewDelhi–110025,India 103PenangRoad,#05–06/07,VisioncrestCommercial,Singapore238467 CambridgeUniversityPressispartoftheUniversityofCambridge. ItfurtherstheUniversity’smissionbydisseminatingknowledgeinthepursuit ofeducation,learning,andresearchatthehighestinternationallevelsofexcellence. www.cambridge.org Informationonthistitle:www.cambridge.org/9781108792509 DOI:10.1017/9781108877831 (cid:2)c CambridgeUniversityPress2022 Thispublicationisincopyright.Subjecttostatutoryexception andtotheprovisionsofrelevantcollectivelicensingagreements, noreproductionofanypartmaytakeplacewithoutthewritten permissionofCambridgeUniversityPress. Firstpublished2022 PrintedintheUnitedKingdombyTJBooksLimited,PadstowCornwall AcataloguerecordforthispublicationisavailablefromtheBritishLibrary. LibraryofCongressCataloging-in-PublicationData Names:Aluffi,Paolo,1960-editor. Title:Facetsofalgebraicgeometry:acollectioninhonorofWilliam Fulton’s80thbirthday/editedbyPaoloAluffi,FloridaState University,DavidAnderson,OhioStateUniversity,MilenaHering, UniversityofEdinburgh,MirceaMusta¸ta˘,UniversityofMichigan,Ann Arbor,SamPayne,UniversityofTexas,Austin. Description:Cambridge,UnitedKingdom;NewYork,NY:Cambridge UniversityPress,2022.|Series:Londonmathematicalsocietylecture noteseries;472,473|Includesbibliographicalreferences. Identifiers:LCCN2021063035(print)|LCCN2021063036(ebook)| ISBN9781108870061(2volumeset;paperback)|ISBN9781108792509 (volume1;paperback)|ISBN9781108792516(volume2;paperback)| ISBN9781108877831(volume1;epub)|ISBN9781108877855(volume2;epub) Subjects:LCSH:Geometry,Algebraic.|Topology.|BISAC:MATHEMATICS/Topology Classification:LCCQA564.F332022(print)|LCCQA564(ebook)| DDC516.3/5–dc23/eng/20220126 LCrecordavailableathttps://lccn.loc.gov/2021063035 LCebookrecordavailableathttps://lccn.loc.gov/2021063036 ISBN–2VolumeSet978-1-108-87006-1Paperback ISBN–Volume1978-1-108-79250-9Paperback ISBN–Volume2978-1-108-79251-6Paperback CambridgeUniversityPresshasnoresponsibilityforthepersistenceoraccuracyof URLsforexternalorthird-partyinternetwebsitesreferredtointhispublication anddoesnotguaranteethatanycontentonsuchwebsitesis,orwillremain, accurateorappropriate. WededicatethesevolumeswithgratitudeandadmirationtoWilliamFulton, ontheoccasionofhis80thbirthday.Wehopethatthearticlescollectedhere, writtenbycolleagues,friends,andstudents,mayreflectthebreadthofBill’s impactonmathematics,alongwiththedepthofhisenduringinfluenceonall ofuswhohavehadthegreatgoodfortunetolearnfromandbe inspiredbyhim. Contents of Volume 1 ContentsofVolume2 pageix ListofContributors(Volume1) xi ListofContributors(Volume2) xiii 1 PositivityofSegre–MacPhersonClasses 1 PaoloAluffi,LeonardoC.Mihalcea,Jo¨rgSchu¨rmann andChangjianSu 2 Brill–NoetherSpecialCubicFourfoldsofDiscriminant14 29 AsherAuel 3 AutomorphismGroupsofAlmostHomogeneousVarieties 54 MichelBrion 4 TopologyofModuliSpacesofTropicalCurveswith MarkedPoints 77 MelodyChan,SørenGalatiusandSamPayne 5 MirrorSymmetryandSmoothingGorensteinToric Affine3-folds 132 AlessioCorti,MatejFilipandAndreaPetracci 6 VertexAlgebrasofCohFT-type 164 ChiaraDamiolini,AngelaGibneyandNicolaTarasca 7 TheConeTheoremandtheVanishingofChowCohomology 190 DanEdidinandRyanRichey 8 Cayley–BacharachTheoremswithExcessVanishing 202 LawrenceEinandRobertLazarsfeld 9 EffectiveDivisorsonHurwitzSpaces 221 GavrilFarkas vii viii ContentsofVolume1 10 ChowQuotientsofGrassmanniansbyDiagonalSubtori 241 NoahGiansiracusaandXianWu 11 QuantumKirwanforQuantumK-theory 265 E.Gonza´lezandC.Woodward 12 ToricVarietiesandaGeneralizationoftheSpringer Resolution 333 WilliamGraham 13 ToricSurfaces,LinearandQuantumCodes:Secret SharingandDecoding 371 JohanP.Hansen Contents of Volume 2 ContentsofVolume1 pageix ListofContributors(Volume2) xi ListofContributors(Volume1) xiii 14 Stability of Tangent Bundles on Smooth Toric Picard-rank-2 VarietiesandSurfaces 1 MilenaHering,BenjaminNillandHendrikSu¨ß 15 TropicalCohomologywithIntegralCoefficientsfor AnalyticSpaces 26 PhilippJell 16 SchubertPolynomials,PipeDreams,EquivariantClasses, andaCo-transitionFormula 63 AllenKnutson 17 PositivityCertificatesviaIntegralRepresentations 84 KhazhgaliKozhasov,MateuszMichałekandBerndSturmfels 18 OntheCoproductinAffineSchubertCalculus 115 ThomasLam,SeungJinLeeandMarkShimozono 19 Bost–ConnesSystemsandF -structuresinGrothendieck 1 Rings,Spectra,andNoriMotives 147 JoshuaF.Lieber,YuriI.Manin,andMatildeMarcolli 20 NefCyclesonSomeHyperka¨hlerFourfolds 228 JohnChristianOttem 21 HigherOrderPolarandReciprocalPolarLoci 238 RagniPiene ix x ContentsofVolume2 22 Characteristic Classes of Symmetric and Skew-symmetric DegeneracyLoci 254 SutipojPromtapanandRicha´rdRima´nyi 23 EquivariantCohomology,SchubertCalculus,and EdgeLabeledTableaux 284 ColleenRobichaux,HarshitYadavandAlexanderYong 24 GaloisGroupsofComposedSchubertProblems 336 FrankSottile,RobertWilliamsandLiYing 25 AK-theoreticFultonClass 367 RichardP.Thomas
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