Automorphisms in Birational and Affine Geometry: Levico Terme, Italy, October 2012 PDF
Preview Automorphisms in Birational and Affine Geometry: Levico Terme, Italy, October 2012
Springer Proceedings in Mathematics & Statistics Ivan Cheltsov Ciro Ciliberto Hubert Flenner James McKernan Yuri G. Prokhorov Mikhail Zaidenberg E ditors Automorphisms in Birational and Affi ne Geometry Levico Terme, Italy, October 2012 Springer Proceedings in Mathematics & Statistics Volume 79 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. Ivan Cheltsov • Ciro Ciliberto • Hubert Flenner • James McKernan • Yuri G. Prokhorov • Mikhail Zaidenberg Editors Automorphisms in Birational and Affine Geometry Levico Terme, Italy, October 2012 123 Editors IvanCheltsov CiroCiliberto SchoolofMathematics DepartmentofMathematics UniversityofEdinburgh UniversityofRomeTorVergata Edinburgh,UnitedKingdom Rome,Italy HubertFlenner JamesMcKernan FacultyofMathematics DepartmentofMathematics RuhrUniversityBochum UniversityofCaliforniaSanDiego Bochum,Germany LaJolla,California,USA YuriG.Prokhorov MikhailZaidenberg SteklovMathematicalInstitute InstitutFourierdeMathématiques RussianAcademyofSciences UniversitéGrenobleI Moscow,Russia Grenoble,France ISSN2194-1009 ISSN2194-1017(electronic) ISBN978-3-319-05680-7 ISBN978-3-319-05681-4(eBook) DOI10.1007/978-3-319-05681-4 SpringerChamHeidelbergNewYorkDordrechtLondon LibraryofCongressControlNumber:2014941702 MathematicsSubjectClassification(2010):14L30,14E07,14R20,14R10,32M17 ©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 The conference brought together specialists from the birational geometry of pro- jectivevarieties,affinealgebraicgeometry,andcomplexalgebraicgeometry.Topics fromtheseareasincludeMoritheory,Cremonagroups,algebraicgroupactions,and automorphisms. The ensuing talks and the discussions have highlighted the close connections between these areas. The meeting allowed these groups to exchange knowledgeandtolearnmethodsfromadjacentfields.Fordetailedinformationabout thisconference,seehttp://www.science.unitn.it/cirm/GABAG2012.html. The chapters in this book cover a wide area of topics from classical algebraic geometry to birational geometry and affine geometry, with an emphasis on group actionsandautomorphismgroups. Amongthetotalof27chapters,eightgiveanoverviewofanareainoneofthe fields. The otherscontainoriginalcontributions,or mix originalcontributionsand surveys. In the birational part, there are chapters on Fano and del Pezzo fibrations, birationalrigidityandsuperrigidityofFanovarieties,birationalmorphismsbetween threefolds,subgroupsof the Cremona group, Jordan groups, real Cremona group, andarealversionoftheSarkisovprogram. In the part on classical projective geometry, there are chapters devoted to algebraic groups acting on projective varieties, automorphism groups of moduli spaces, and the algebraicity problem for analytic compactifications of the affine plane. The topics in affine geometry include: different aspects of the automorphism groups of affine varieties, flexibility properties in affine algebraic and analytic geometry,automorphismsof affinespaces andShestakov–Umirbaevtheory,affine geometry in positive characteristic, the automorphism groups of configuration spacesandotherclassesofaffinevarietiesanddeformationsofcertaingroupactions onaffinevarieties. Hopefully these proceedingswill be of help for both specialists, who will find information on the current state of research, and young researchers, who wish to learnaboutthesefascinatingandactiveareasofmathematics. v vi Preface Acknowledgments The editors would like to thank the contributorsof this volume.They are grateful to the CIRM at Trento, its directors Marco Andreatta and Fabrizio Catanese, its secretary Augusto Micheletti, and the whole staff for their permanent support in the organization of the conference and the distribution of this volume. Our thanks are due also to Marina Reizakis, Frank Holzwarth, and the staff of the Springerpublishinghouse for agreeablecooperationduringthe preparationof the proceedings. Edinburgh,UK IvanCheltsov Rome,Italy CiroCiliberto Bochum,Germany HubertFlenner LaJolla,CA JamesMcKernan Moscow,Russia YuriG.Prokhorov Grenoble,France MikhailZaidenberg Contents PartI BirationalAutomorphisms SingulardelPezzoFibrationsandBirationalRigidity....................... 3 HamidAhmadinezhad AdditiveActionsonProjectiveHypersurfaces................................ 17 IvanArzhantsevandAndreyPopovskiy CremonaGroupsofRealSurfaces............................................. 35 JérémyBlancandFrédéricMangolte OnAutomorphismsandEndomorphismsofProjectiveVarieties.......... 59 MichelBrion DelPezzoSurfacesandLocalInequalities .................................... 83 IvanCheltsov FanoHypersurfacesandtheirBirationalGeometry......................... 103 TommasodeFernex OntheLocusofNonrigidHypersurfaces ..................................... 121 ThomasEcklandAleksandrPukhlikov OntheGenusofBirationalMapsBetweenThreefolds...................... 141 StéphaneLamy OntheAutomorphismsofModuliSpacesofCurves......................... 149 AlexMassarentiandMassimilianoMella NormalAnalyticCompactificationsofC2..................................... 169 PinakiMondal JordanGroupsandAutomorphismGroupsofAlgebraicVarieties........ 185 VladimirL.Popov vii viii Contents 2-ElementarySubgroupsoftheSpaceCremonaGroup..................... 215 YuriProkhorov BirationalAutomorphismGroupsof ProjectiveVarieties ofPicardNumberTwo .......................................................... 231 De-QiZhang PartII AutomorphismsofAffineVarieties RationalCurveswithOnePlaceatInfinity ................................... 241 AbdallahAssi The Jacobian Conjecture, Together with Specht andBurnside-TypeProblems................................................... 249 AlexeiBelov,LeonidBokut,LouisRowen,andJie-TaiYu Equivariant Triviality of Quasi-Monomial Triangular G -ActionsonA4................................................................. 287 a AdrienDubouloz,DavidR.Finston,andImadJaradat AutomorphismGroupsofCertainRationalHypersurfaces inComplexFour-Space.......................................................... 301 AdrienDubouloz,LucyMoser-Jauslin,andPierre-MariePoloni LaurentCancellationforRingsofTranscendenceDegreeOne OveraField....................................................................... 313 GeneFreudenburg DeformationsofA1-Fibrations ................................................. 327 RajendraV.Gurjar,KayoMasuda,andMasayoshiMiyanishi RemarkonDeformationsofAffineSurfaceswithA1-Fibrations........... 363 TakashiKishimoto HowtoProvetheWildnessofPolynomialAutomorphisms: AnExample....................................................................... 381 ShigeruKuroda Flexibility Properties in Complex Analysis and Affine AlgebraicGeometry ............................................................. 387 FrankKutzschebauch StronglyResidualCoordinatesoverAŒx(cid:2) ..................................... 407 DrewLewis Configuration Spaces of the Affine Line and their AutomorphismGroups.......................................................... 431 VladimirLinandMikhailZaidenberg Contents ix OntheNewtonPolygonofaJacobianMate .................................. 469 LeonidMakar-Limanov KellerMapsofLowDegreeoverFiniteFields................................ 477 StefanMaubachandRoelWillems Cancellation....................................................................... 495 PeterRussell
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