LONDONMATHEMATICALSOCIETYLECTURENOTESERIES ManagingEditor:ProfessorEndreSu¨li,MathematicalInstitute,UniversityofOxford, WoodstockRoad,OxfordOX26GG,UnitedKingdom Thetitlesbelowareavailablefrombooksellers,orfromCambridgeUniversityPressat www.cambridge.org/mathematics 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¸Aˇ&M.POPA(eds) 418 TheBloch–KatoconjecturefortheRiemannzetafunction, J.COATES,A.RAGHURAM, A.SAIKIA&R.SUJATHA(eds) Published online by Cambridge University Press 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.KEDZIOREK&M.SZYMIK(eds) 475 EffectiveresultsandmethodsforDiophantineequationsoverfinitelygenerateddomains, J.-H.EVERTSE&K.GYO˝RY 476 Anindefiniteexcursioninoperatortheory, A.GHEONDEA 477 EllipticRegularityTheorybyApproximationMethods, E.A.PIMENTEL Published online by Cambridge University Press LondonMathematicalSocietyLectureNoteSeries:478 Recent Developments in Algebraic Geometry ToMilesReidforhis70thBirthday Editedby HAMID ABBAN LoughboroughUniversity GAVIN BROWN UniversityofWarwick ALEXANDER KASPRZYK UniversityofNottingham SHIGEFUMI MORI KyotoUniversity Published online by Cambridge University Press 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 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ItfurtherstheUniversity’smissionbydisseminatingknowledgeinthepursuitof education,learning,andresearchatthehighestinternationallevelsofexcellence. www.cambridge.org Informationonthistitle:www.cambridge.org/9781009180856 DOI:10.1017/9781009180849 (cid:2)c CambridgeUniversityPress2022 Thispublicationisincopyright.Subjecttostatutoryexception andtotheprovisionsofrelevantcollectivelicensingagreements, noreproductionofanypartmaytakeplacewithoutthewritten permissionofCambridgeUniversityPress. Firstpublished2022 PrintedintheUnitedKingdombyTJBooksLimited,PadstowCornwall AcataloguerecordforthispublicationisavailablefromtheBritishLibrary. LibraryofCongressCataloging-in-PublicationData Names:Abban,Hamid,1983–author.|Brown,Gavin,1968–author.| Kasprzyk,Alexander,1980–author.|Mori,Shigefumi,author. Title:Recentdevelopmentsinalgebraicgeometry:toMilesReidforhis 70thbirthday/editedbyHamidAbban,LoughboroughUniversity,Gavin Brown,UniversityofWarwick,AlexanderKasprzyk,Universityof Nottingham,ShigefumiMori,KyotoUniversity. Description:Cambridge,UnitedKingdom;NewYork,NY,USA:Cambridge UniversityPress,2022.|Includesbibliographicalreferencesandindex. Identifiers:LCCN2022009684|ISBN9781009180856(paperback)| ISBN9781009180849(ebook) Subjects:LCSH:Reid,Miles(MilesA.)–Influence.|Geometry,Algebraic. Classification:LCCQA564.A1982022|DDC516.3/5–dc23/eng20220716 LCrecordavailableathttps://lccn.loc.gov/2022009684 ISBN978-1-009-18085-6Paperback CambridgeUniversityPresshasnoresponsibilityforthepersistenceoraccuracyof URLsforexternalorthird-partyinternetwebsitesreferredtointhispublication anddoesnotguaranteethatanycontentonsuchwebsitesis,orwillremain, accurateorappropriate. Published online by Cambridge University Press 70 Miles Published online by Cambridge University Press Published online by Cambridge University Press Contents ListofContributors pageix Happy Birthday HamidAbban,GavinBrown,AlexanderKasprzykandShigefumiMori 1 On Stable Cohomology of Central Extensions of Elementary Abelian Groups Fedor Bogomolov, Christian B¨ohning and Alena Pirutka 4 On Projective 3-Folds of General Type with p = 2 g Meng Chen, Yong Hu and Matteo Penegini 20 15-Nodal Quartic Surfaces. Part I: Quintic del Pezzo Surfaces and Congruences of Lines in P3 Igor V. Dolgachev 66 Mori Flips, Cluster Algebras and Diptych Varieties Without Unprojection Tom Ducat 116 The Mirror of the Cubic Surface Mark Gross, Paul Hacking, Sean Keel and Bernd Siebert 150 Semi-Orthogonal Decomposition of a Derived Category of a 3-Fold With an Ordinary Double Point Yujiro Kawamata 183 Duality and Normalization, Variations on a Theme of Serre and Reid J´anos Kolla´r 216 Published online by Cambridge University Press viii Contents Rationality of Q-Fano Threefolds of Large Fano Index Yuri Prokhorov 253 An Exceptional Locus in the Perfect Compactification of A g N. I. Shepherd-Barron 275 Variation of Stable Birational Types of Hypersurfaces Evgeny Shinder 296 Triangle Varieties and Surface Decomposition of Hyper-K¨ahler Manifolds Claire Voisin 314 Published online by Cambridge University Press Contributors HamidAbban DepartmentofMathematicalSciences,LoughboroughUniversity JohnArmstrong DepartmentofMathematics,King’sCollegeLondon FedorBogomolov CourantInstituteofMathematicalSciences,NewYorkUniversity ChristianBo¨hning MathematicsInstitute,UniversityofWarwick GavinBrown MathematicsInstitute,UniversityofWarwick MengChen SchoolofMathematicalSciences,FudanUniversity HailongDao DepartmentofMathematics,UniversityofKansas IgorV.Dolgachev DepartmentofMathematics,UniversityofMichigan TomDucat MathematicalSciences,DurhamUniversity MarkGross TheDepartmentofPureMathematicsandMathematicalStatistics, UniversityofCambridge PaulHacking DepartmentofMathematicsandStatistics,UniversityofMassachusetts Published online by Cambridge University Press