代数几何:Algebraic Geometry

代数几何:Algebraic Geometry
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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
180人买过
  • 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
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