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1、INTRODUCTIONTOALGEBRAICGEOMETRYBYDR.B.L.VANDERWAERDENO.PROFESSOROFMATHEMATICSATTHEUNIVERSITYOFLEIPZIGTRANSLATEDBYD.H.DELPHENICHWITH15FIGURESPUBLISHEDANDDISTRIBUTEDINTHEPUBLICINTERESTBYAUTHORITYOFTHEU.S.ALIENPROPERTYCUSTODIANUNDERLICENSENO.A-698NEWYORKDOVERPUBLICATIONS1945ALLRIGHTSRESERVED,INPA
2、RTICULAR,THETRANSLATIONINTOFOREIGNLANGUAGES.COPYRIGHT1939BYJULIANSPRINGERINBERLINCOPYRIGHTVESTEDINTHEU.S.ALIENPROPERTYCUSTODIAN1944,PURSUANTTOLAWFIRSTAMERICANEDITIONPRINTEDINTHEUNITEDSTATESOFAMERICAFOREWORDFromthelecturesintheworthwhileErgebnissetextbook“AlgebraicSurfaces”byO.ZARISKI,thethough
3、tofwritinganintroductiontoalgebraicgeometrytookonadefiniteformforme.Suchanintroductionshouldcontainthe“elements”ofalgebraicgeometryintheclassicalsenseoftheword;i.e.,itshouldprovidethenecessaryfoundationsforgoingfurtherintothedeepertheory.Also,HerrGEPPERT,whointendedtowriteabookonalgebraicsurfa
4、cesinthiscollection,emphasizedthenecessityofsuchanintroduction,towhichhecouldthenrefer,andencouragedmetowritethisbook.WhatIlearnedinthecourseofmyownverysubstantiallecturesonalgebraiccurvesandsurfacesprovedusefultomeintheprocessofwriting;IcanthereforeemployalecturepreparationthatwaspreparedbyDr
5、.M.DEURINGandDr.V.GARTEN.Thus,muchmaterialwasborrowedfrommyseriesofarticlesintheMathematischenAnnalen“ZuralgebraischenGeometrie.”Inthechoiceofmaterial,itwasnottheaestheticviewpoint,butultimatelythedistinctionbetweenbeingnecessaryandbeingdispensablethatwasdefinitive.Everythingthatisderivedfromt
6、he“elements”withoutqualificationwillhavetobe,Ihope,assumed.Thetheoryofideals,whichledmetomyearlierinvestigations,seemstobedispensableforlayingthegroundwork;thefar-reachingmethodsoftheItalianschoolwilltakeitsplace.Fortheexplanationofthemethodsandextensionoftheproblemstatementsubstantialindividu
7、algeometricproblemswouldhavetobeaddressed;forthatreason,Ihavealsosoughttorestrictthatextensiontoacertaindegreehere,sinceotherwisethescopewouldeasilygrowwithoutbound.IwasassistedinthecorrectionprocessbyHerrenProf.H.GEPPERT,Dr.O.-H.KELLER
