代数几何:Algebraic Geometry

代数几何:Algebraic Geometry
分享
扫描下方二维码分享到微信
打开微信,点击右上角”+“,
使用”扫一扫“即可将网页分享到朋友圈。
作者:
1999-11
版次: 1
ISBN: 9787506200820
定价: 82.00
装帧: 平装
开本: 24开
纸张: 胶版纸
页数: 496页
正文语种: 英语
分类: 自然科学
  • Thisbookprovidesanintroductiontoabstractalgebraicgeometryusingthemethodsofschemesandcohomology.Themainobjectsofstudyarealgebraicvarietiesinanaffineorprojectivespaceoveranalgebraicallyclosedfield;theseareintroducedinChapterI,toestablishanumberofbasicconceptsandexamples.ThenthemethodsofschemesandcohomologyaredevelopedinChaptersIIandIII,withemphasisonapplicationsratherthanexcessivegenerality.Thelasttwochaptersofthebook(IVandV)usethesemethodstostudytopicsintheclassicaltheoryofalgebraiccurvesandsurfaces. Introduction
    CHAPTERIVarieties
    1AffineVarieties
    2ProjectiveVarieties
    3Morphisms
    4RationalMaps
    5NonsingularVarieties
    6NonsingularCurves
    7IntersectionsinProjectiveSpace
    8WhatIsAlgebraicGeometry?

    CHAPTERIISchemes
    1Sheaves
    2Schemes
    3FirstPropertiesofSchemes
    4SeparatedandProperMorphisms
    5SheavesofModules
    6Divisors
    7ProjectiveMorphisms
    8Differentials
    9FormalSchemes

    CHAPTERIIICohomology
    1DerivedFunctors
    2CohomologyofSheaves
    3CohomologyofaNoetherianAffineScheme
    4CechCohomology
    5TheCohomologyofProjectiveSpace
    6ExtGroupsandSheaves
    7TheSerreDualityTheorem
    8HigherDirectimagesofSheaves
    9FlatMorphisms
    10SmoothMorphisms
    11TheTheoremonFormalFunctions
    12TheSemicontinuityTheorem

    CHAPTERIVCurves
    1Riemann-RochTheorem
    2HurwitzsTheorem
    3EmbeddingsinProjectiveSpace
    4EllipticCarves
    5TheCanonicalEmbedding
    6ClassificationofCurvesinP3

    CHAPTERVSurfaces
    1GeometryonaSurface
    2RuledSurfaces
    3MonoidalTransformations
    4TheCubicSurfaceinP3
    5BirationalTransformations
    6ClassificationofSurfaces
    APPENDIXA
    APPENDIXB
    APPENDIXC
    Bibliography
    ResultsfromAlgebra
    GlossaryofNotations
    Index
  • 内容简介:
    Thisbookprovidesanintroductiontoabstractalgebraicgeometryusingthemethodsofschemesandcohomology.Themainobjectsofstudyarealgebraicvarietiesinanaffineorprojectivespaceoveranalgebraicallyclosedfield;theseareintroducedinChapterI,toestablishanumberofbasicconceptsandexamples.ThenthemethodsofschemesandcohomologyaredevelopedinChaptersIIandIII,withemphasisonapplicationsratherthanexcessivegenerality.Thelasttwochaptersofthebook(IVandV)usethesemethodstostudytopicsintheclassicaltheoryofalgebraiccurvesandsurfaces.
  • 目录:
    Introduction
    CHAPTERIVarieties
    1AffineVarieties
    2ProjectiveVarieties
    3Morphisms
    4RationalMaps
    5NonsingularVarieties
    6NonsingularCurves
    7IntersectionsinProjectiveSpace
    8WhatIsAlgebraicGeometry?

    CHAPTERIISchemes
    1Sheaves
    2Schemes
    3FirstPropertiesofSchemes
    4SeparatedandProperMorphisms
    5SheavesofModules
    6Divisors
    7ProjectiveMorphisms
    8Differentials
    9FormalSchemes

    CHAPTERIIICohomology
    1DerivedFunctors
    2CohomologyofSheaves
    3CohomologyofaNoetherianAffineScheme
    4CechCohomology
    5TheCohomologyofProjectiveSpace
    6ExtGroupsandSheaves
    7TheSerreDualityTheorem
    8HigherDirectimagesofSheaves
    9FlatMorphisms
    10SmoothMorphisms
    11TheTheoremonFormalFunctions
    12TheSemicontinuityTheorem

    CHAPTERIVCurves
    1Riemann-RochTheorem
    2HurwitzsTheorem
    3EmbeddingsinProjectiveSpace
    4EllipticCarves
    5TheCanonicalEmbedding
    6ClassificationofCurvesinP3

    CHAPTERVSurfaces
    1GeometryonaSurface
    2RuledSurfaces
    3MonoidalTransformations
    4TheCubicSurfaceinP3
    5BirationalTransformations
    6ClassificationofSurfaces
    APPENDIXA
    APPENDIXB
    APPENDIXC
    Bibliography
    ResultsfromAlgebra
    GlossaryofNotations
    Index
查看详情
其他版本 / 全部 (1)
相关图书 / 更多
代数几何:Algebraic Geometry
代数的魅力与技巧
单墫 著
代数几何:Algebraic Geometry
代数数论简史(精)/中外数学史研究丛书
冯克勤 著
代数几何:Algebraic Geometry
代数学引论第三版
聂灵沼、丁石孙 著
代数几何:Algebraic Geometry
代数与数论:综合方法(英文)
[美]马丁.R.狄克逊
代数几何:Algebraic Geometry
代数学基础(第2版)上册
张英伯 王恺顺 著;北京师范大学数学科学学院 编
代数几何:Algebraic Geometry
代数分析
[英]卢瑟福 著
代数几何:Algebraic Geometry
代数(盖尔范德中学生数学思维丛书)
I.、M.、Gelfand、A.、Shen 著
代数几何:Algebraic Geometry
代数的历史 人类对未知量的不舍追踪 修订版
[美]约翰·德比希尔(John Derbyshire)
代数几何:Algebraic Geometry
代数、生物信息和机器人技术的算法问题.第六卷,恒等式和准恒等式的相等问题、可推导性和可实现性(俄文)
[俄罗斯]弗拉基米尔·波波夫 著
代数几何:Algebraic Geometry
代数溯源——花拉子密《代数学》研究
郭园园 著
代数几何:Algebraic Geometry
代数几何学原理III.凝聚层的上同调
Alexander、Grothe 著
代数几何:Algebraic Geometry
代数、生物信息和机器人技术的算法问题:第四卷,独立恒等式系统(俄文)
[俄罗斯]弗拉基米尔·波波夫 著
您可能感兴趣 / 更多
代数几何:Algebraic Geometry
宗教与资本主义的兴起
R.H.托尼 著;赵月瑟、夏镇平 译
代数几何:Algebraic Geometry
脊柱外科技术
R.Haher 著;党耕町 译
代数几何:Algebraic Geometry
哈佛商学案例精选集 实务系列
R.H.海伊
代数几何:Algebraic Geometry
生物制药业
R.H.海伊斯
代数几何:Algebraic Geometry
罗马人
R.H.巴洛
代数几何:Algebraic Geometry
生态学及群体生物发展中的VOLTERRA-HAMILTON模型VOLTERRA-HAMILTON MODELS IN
R.H.Bradbury