资源描述：
《noncommutative curves and noncommutative surfaces》由会员上传分享，免费在线阅读，更多相关内容在教育资源-天天文库。
1、BULLETIN(NewSeries)OFTHEAMERICANMATHEMATICALSOCIETYVolume38,Number2,Pages171{216S0273-0979(01)00894-1ArticleelectronicallypublishedonJanuary9,2001NONCOMMUTATIVECURVESANDNONCOMMUTATIVESURFACESJ.T.STAFFORDANDM.VANDENBERGHAbstract.Inthissurveyarticlewedescribesomegeometricr
2、esultsinthetheoryofnoncommutativeringsand,moregenerally,inthetheoryofabeliancategories.Roughlyspeakingandbyanalogywiththecommutativesituation,thecat-egoryofgradedmodulesmodulotorsionoveranoncommutativegradedringofquadratic,respectivelycubic,growthshouldbethoughtofastheno
3、ncom-mutativeanalogueofaprojectivecurve,respectivelysurface.Thisintuitionhasledtoaremarkablenumberofnontrivialinsightsandresultsinnoncom-mutativealgebra.Indeed,theproblemofclassifyingnoncommutativecurves(andnoncommutativegradedringsofquadraticgrowth)canberegardedassettle
4、d.Despitethefactthatnoclassi cationofnoncommutativesurfacesisinsight,arichbodyofnontrivialexamplesandtechniques,includingblowingupanddown,hasbeendeveloped.Contents1.Introduction1722.Geometricconstructions1773.Twistedhomogeneouscoordinaterings1804.Algebraswithlineargrowth
5、1825.NoncommutativeprojectivecurvesI:Domainsofquadraticgrowth1836.NoncommutativeprojectivecurvesII:Primerings1867.Noncommutativesmoothpropercurves1898.Artin-Schelterregularalgebras1949.Commutativesurfaces19810.Noncommutativesurfaces20011.Noncommutativeprojectiveplanesand
6、quadrics20212.P1-Bundles20613.Noncommutativeblowingup208Index213References213ReceivedbytheeditorsOctober18,1999,andinrevisedformMay20,2000.2000MathematicsSubjectClassi cation.Primary14A22,14F05,16D90,16P40,16S80,16W50,18E15.Keywordsandphrases.Noetheriangradedrings,noncom
7、mutativeprojectivegeometry,de-formations,twistedhomogeneouscoordinaterings.The rstauthorwassupportedinpartbyanNSFgrant.ThesecondauthorisaseniorresearcherattheFWOandwaspartiallysupportedbytheClayResearchInstituteduringthepreparationofthisarticle.c2001AmericanMathematicalS
8、ociety171172J.T.STAFFORDANDM.VANDENBERGH1.IntroductionIthasalwaysbeenclearthatnoncommutativeringsaremuc
