代数几何原理
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作者[美]P.格里菲思,J.哈里斯
出版社世界图书出版公司
ISBN9787519260705
出版时间2019-05
版次1
装帧平装
开本16开
纸张胶版纸
定价149元
上书时间2024-08-04
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基本信息
书名:代数几何原理
定价：149.00元
作者:[美]P.格里菲思,J.哈里斯
出版社：世界图书出版公司
出版日期：2019-05-01
ISBN：9787519260705
字数：
页码：
版次：
装帧：平装
开本：16开
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内容提要
代数几何是数学中古老和发展比较快的学科之一，它与投影几何、复分析、拓扑学、数论以及数学领域的其它分支有着紧密的联系。然而近些年代数几何不论是风格还是语言都发生了巨大的变化，本书展示了相关理论的主要研究结果和计算工具的发展。本书有如下特点：（1）本书以研究具体几何问题和特殊类代数簇为中心来展开。（2）注重实例的复杂性与通常模式的对称性这两者之间的均衡，在选择的论题和叙述顺序中，书中尽量体现这种关系。（3）尤其对于涉及到的“复杂”结果，都有充分完整的证明。目次：多复变初步；复代数簇；Liemann曲面和代数曲线；深入技巧；曲面；留数；二次线丛。
目录
CHAPTER 0 FOUNDATIONAL MATERIAL1. Rudiments of Several Complex VariablesCauchy's Formula and ApplicationsSeveral VariablesWeierstrass Theorems and CorollariesAnalytic Varieties2. Complex ManifoldsComplex ManifoldsSubmanifolds and SubvarietiesDe Rham and Dolbeault CohomologyCalculus on Complex Manifolds3. Sheaves and CohomologyOrigins: The Mittag-Leffler ProblemSheavesCohomology of SheavesThe de Rham TheoremThe Dolbeault Theorem4. Topology of ManifoldsIntersection of CyclesPoincare DualityIntersection of Analytic Cycles5. Vector Bundles, Connections, and CurvatureComplex and Holomorphic Vector BundlesMetrics, Connections, and Curvature6. Harmonic Theory on Compact Complex ManifoldsThe Hodge TheoremProof of the Hodge Theorem I: Local TheoryProof of the Hodge Theorem II: Global TheoryApplications of the Hodge Theorem7. Kahler ManifoldsThe Kahler ConditionThe Hodge Identities and the Hodge DecompositionThe Lefschetz DecompositionCHAPTER 1 COMPLEX ALGEBRAIC VARIETIES1. Divisors and Line BundlesDivisorsLine BundlesChern Classes of Line Bundles2. Some Vanishing Theorems and CorollariesThe Kodaira Vanishing TheoremThe Lefschetz Theorem on Hyperplane SectionsTheorem BThe Lefschetz Theorem on (1, l)-classes3. Algebraic VarietiesAnalytic and Algebraic VarietiesDegree of a VarietyTangent Spaces to Algebraic Varieties4. The Kodaira Embedding TheoremLine Bundles and Maps to Projective SpaceBlowing UpProof of the Kodaira Theorem5. GrassmanniansDefinitionsThe Cell DecompositionThe Schubert CalculusUniversal BundlesThe Pliicker EmbeddingCHAPTER 2 RIEMANN SURFACES AND ALGEBRAICCURVESPreliminariesEmbedding Riemann SurfacesThe Riemann-Hurwitz FormulaThe Genus FormulaCases g=0, 12. Abel's TheoremAbel's Theorem——First VersionThe First Reciprocity Law and CorollariesAbel's Theorem——Second VersionJacobi Inversion3. Linear Systems on CurvesReciprocity Law IIThe Riemann-Roch FormulaCanonical CurvesSpecial Linear Systems IHyperelliptic Curves and Riemann's CountSpecial Linear Systems II4. Plucker FormulasAssociated CurvesRamificationThe General Plucker Formulas IThe General Plucker Formulas IIWeierstrass PointsPlucker Formulas for Plane Curves5. CorrespondencesDefinitions and FormulasGeometry of Space CurvesSpecial Linear Systems III6. Complex Tori and Abelian VarietiesThe Riemann ConditionsLine Bundles on Complex ToriTheta-FunctionsThe Group Structure on an Abelian VarietyIntrinsic Formulations7. Curves and Their JacobiansPreliminariesRiemann's TheoremRiemann's Singularity TheoremSpecial Linear Systems IVTorelli's TheoremCHAPTER 3 FURTHER TECHNIQUES1. Distributions and CurrentsDefinitions; Residue FormulasSmoothing and RegularityCohomology of Currents2. Applications of Currents to Complex AnalysisCurrents Associated to Analytic VarietiesIntersection Numbers of Analytic VarietiesThe Levi Extension and Proper Mapping Theorems3. Chern ClassesDefinitionsThe Gauss Bonnet FormulasSome Remarks——Not Indispensable——ConcerningChern Classes of Holomorphic Vector Bundles4. Fixed-Point and Residue FormulasThe Lefschetz Fixed-Point FormulaThe Holomorphic Lefschetz Fixed-Point FormulaThe Bott Residue FormulaThe General Hirzebruch-Riemann-Roch Formula5. Spectral Sequences and ApplicationsSpectral Sequences of Filtered and Bigraded ComplexesHypercohomologyDifferentials of the Second KindThe Leray Spectral SequenceCHAPTER 4 SURFACES1. PreliminariesIntersection Numbers, the Adjunction Formula,and Riemann-RochBlowing Up and DownThe Quadric SurfaceThe Cubic Surface2. Rational MapsRational and Birationai MapsCurves on an Algebraic SurfaceThe Structure of Birational Maps Between Surfaces3. Rational Surfaces INoether's LemmaRational Ruled SurfacesThe General Rational SurfaceSurfaces of Minimal DegreeCurves of Maximal GenusSteiner ConstructionsThe Enriques-Petri Theorem4. Rational Surfaces IIThe Castelnuovo-Enriques TheoremThe Enriques SurfaceCubic Surfaces RevisitedThe Intersection of Two Quadrics in p45. Some Irrational SurfacesThe Albanese MapIrrational Ruled SurfacesA Brief Introduction to Elliptic SurfacesKodaira Number and the Classification Theorem IThe Classification Theorem IIK-3 SurfacesEnriques Surfaces6. Noether's FormulaNoether's Formula for Smooth HypersurfacesBlowing Up SubmanifoldsOrdinary Singularities of SurfacesNoether's Formula for General SurfacesSome ExamplesIsolated Singularities of SurfacesCHAPTER 5 RESIDUES1. Elementary Properties of ResiduesDefinition and Cohomological InterpretationThe Global Residue TheoremThe Transformation Law and Local Duality2. Applications of ResiduesIntersection NumbersFinite Holomorphic MappingsApplications to Plane Projective Geometry3. Rudiments of Commutative and Homological Algebrawith ApplicationsCommutative AlgebraHomological AlgebraThe Koszul Complex and ApplicationsA Brief Tour Through Coherent Sheaves4. Global DualityGlobal ExtExplanation of the General Global Duality TheoremGlobal Ext and Vector Fields with Isolated ZerosGlobal Duality and Superabundance ofPoints on a SurfaceExtensions of ModulesPoints on a Surface and Rank-Two Vector BundlesResidues and Vector BundlesCHAPTER 6 THE QUADRIC LINE COMPLEX1. Preliminaries: QuadricsRank of a QuadricLinear Spaces on QuadricsLinear Systems of QuadricsLines on Linear Systems of QuadricsThe Problem of Five Conics2. The Quadric Line Complex: IntroductionGeometry of the Grassmannian G(2,4)Line ComplexesThe Quadric Line Complex and Associated Kummer Surface ISingular Lines of the Quadric Line ComplexTwo Configurations3. Lines on the Quadric Line ComplexThe Variety of Lines on the Quadric Line ComplexCurves on the Variety of LinesTwo Configurations RevisitedThe Group Law4. The Quadric Line Complex: RepriseThe Quadric Line Complex and Associated Kummer Surface IIRationality of the Quadric Line ComplexINDEX
作者介绍
Phillip Griffiths , Joseph Harris（P. 格里菲思，美国；J. 哈里斯，美国）是美国哈佛大学教授。
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