代数几何．1，代数曲线，代数流形与概型

Ⅰ.RiemannSurfacesandAlgebraicCurves

V.V.Shokurov

Ⅱ.AlgebraicVarietiesandSchemes

V.I.Danilov

AuthorIndex

SubjectIndex

　　本书是一部全面介绍代数曲线、代数流形的教程（全英文版）。主体内容有两部分组成：一部分以V.V.Shokurov所写的学术著作为蓝本，主要讲述黎曼面和代数曲面理论，深刻地揭示了黎曼面和其模型复射影面中的复代数曲面的相互关系；另外一部分以V.I.Danilov的学术论文为蓝本主要讨论了代数变量及其概型。本书结构框架清晰，叙述简明扼要，可以帮助读者在很短的时间内了解并掌握代数几何的精华。　　Thisbookconsistsoftwoparts.Thefirstisdevotedtothetheoryofcurves,whicharetreatedfromboththeanalyticandalgebraicpointsofview.StartingwiththebasicnotionsofthetheoryofRiemannsurfacesthereaderisleadintoanexpositioncoveringtheRiemann-Rochtheorem,Riemannsfundamentalexistencetheorem.uniformizationandautomorphicfunctions.ThealgebraicmaterialalsotreatsalgebraiccurvesoveranarbitraryfieldandtheconnectionbetweenalgebraiccurvesandAbelianvarieties.Thesecondpartisanintroductiontohigher-dimensionalalgebraicgeometry.Theauthordealswithalgebraicvarieties,thecorrespondingmorphisms,thetheoryofcoherentsheavesand,finally,Thetheoryofschemes.Thisbookisaveryreadableintroductiontoalgebraicgeometryandwillbeimmenselyusefultomathematiciansworkinginalgebraicgeometryandcomplexanalysisandespeciallytograduatestudentsinthesefields.