代数几何原理

Athirdgeneralprinciplewasthatthisvolumeshouldbestir-contained.Inparticularany"hard"resultthatwouldbeutilizedshouldbefullyproved.Adifficultyastudentoftenfacesinasubjectasdiverseasalgebraicgeometryistheprofusionofcross-references,andthisisonereasonforattemptingtobeself-contained.Similarly,wehaveattemptedtoavoidallusionsto,orstatementswithoutproofsof,relatedresults.Thisbookisinnowaymeanttobeasurveyofalgebraicgeometry,butratherisdesignedtodevelopaworkingfacilitywithspecificgeometricquestions.Ourapproachtothesubjectisinitiallyanalytic：Chapters0and1treatthebasictechniquesandresultsofcomplexmanifoldtheory,withsomeemphasisonresultsapplicabletoprojectivevarieties.BeginninginChapter2withthetheoryofRiemannsurfacesandalgebraiccurves,andcontinu-inginChapters4and6onalgebraicsurfacesandthequadriclinecomplex,ourtreatmentbecomesincreasinglygeometricalongclassicallines.Chapters3and5continuetheanalyticapproach,progressingtomorespecialtopicsincomplexmanifolds.