资源描述：
《Complex Abelian Varieties and Theta Functions》由会员上传分享，免费在线阅读，更多相关内容在学术论文-天天文库。
1、GeorgeR.KempfComplexAbelianVarietiesandThetaFunctionsSpringer-VerlagBerlinHeidelbergNewYorkLondonParisTokyoHongKongBarcelonaGeorgeR.KempfDepartmentofMathematicsJohnHopkinsUniversityBaltimore,MD21218,USAMathematicsSubjectClassification(1980):14K20,14K25,32C35,32125,32N05ISBN3-540-53168-
2、8Springer-VerlagBerlinHeidelbergNewYorkISBN0-387-53168-8Springer-VerlagNewYorkBerlinHeidelbergLibraryofCongressCataloging-m-PublicationDataKempf,GeorgeComplcxabelianvarietiesandthetafunctions/GeorgeRKcmpfp.cm-(Universitext)IncludesbibliographicalreferencesandindexISBN0-387-53168-8-ISBN
3、3-540-53168-81.Abelianvarieties.2Functions,ThetaITitleQA564K4519905163'53-dc2090-22573CIPTillsworkissubjecttocopynght.Allrightsarereserved,whetherthewholeorpartofthematenalisconcerned,specificallythenghtsoftranslation,repnnting,reuse01illus•trations,recitation,broadcasting,reproduction
4、onmicrofilmsorinother\ays,andstoragemdatabanksDuplicationofthispublicationorpartsthereofisonlypermittedundertheprovisionsoftheGermanCopynghtLawofSeptember9,1965,initscurrentversion,andacopynghtfeemustalwaysbeprudViolationsfallundertheprosecutionactoftheGermanCopyrightLaw©Springer-Verl
5、agBerlinHeidelberg1991PrintedmGermany4113140-543210-Pnntedonacid-freepaperPrefaceThestudyofabelianvarietiesbeganwiththeone-dimensionalcaseofellipticcurves.Assuchcill'vesaredefinedbyageneralcubicpolynomialequationintwovariables,theirstudyisbasictoallbutthesimplestmathematic!:>.Themodern
6、approachtoellipticcurvesoccurredinthebeginningofthenineteencenturywiththeworkofGauss,AbelandJacobi.Sincetheclassicalperiodtherehavebeenmanydevelopmentsinmathemat•ics.Therearebasicallytwodistinctlinesofgeneralizationofanellipticcurve.Theyarealgebraiccurvesofhighergenus'>1.Theotherishigh
7、erdimensionalcompactalgebraicgroups(abelianvarieties).Thisbookdealswiththesehigherdimensionalobjectswhichsurprisinglyenoughhavemoresimilarpropertiestoellipticcurvesthancurvesofhighergenus.Therearethreemethodsforstudyingabelianvarieties:arithmetic,al•gebraicandanalytic.Thearithmeticst
