代数几何：Algebraic Geometry

图书标准信息

• 作者 R.Hartshorne 著
• 出版社 世界图书出版公司
• 出版时间 1999-11
• 版次 1
• ISBN 9787506200820
• 定价 82.00元
• 装帧 平装
• 开本 24开
• 纸张 胶版纸
• 页数 496页
• 正文语种 英语

【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