代数几何基础教程

图书标准信息

• 作者 J.Harris 编
• 出版社 世界图书出版公司
• 出版时间 2000-06
• 版次 1
• ISBN 9787506247146
• 定价 59.00元
• 装帧 平装
• 开本 24开
• 纸张 胶版纸
• 页数 328页

【内容简介】

Thisbookisbasedonone-semestercoursesgivenatHarvardin1984,atBrownin1985,andatHarvardin1988.Itisintendedtobe,asthetitlesuggests,afirstintroductiontothesubject.Evenso,afewwordsareinorderaboutthepurposesofthebook.Algebraicgeometryhasdevelopedtremendouslyoverthelastcentury.Duringthe19thcentury,thesubjectwaspracticedonarelativelyconcrete,down-to-earthlevel;themainobjectsofstudywereprojectivevarieties,andthetechniquesforthemostpartweregroundedingeometricconstructions.ThisapproachflourishedduringthemiddleofthecenturyandreacheditsculminationintheworkoftheItalianschoolaroundtheendofthe19thandthebeginningofthe20thcenturies.Ultimately,thesubjectwaspushedbeyondthelimitsofitsfoundations:bytheendofitsperiodtheItalianschoolhadprogressedtothepointwherethelanguageandtechniquesofthesubjectcouldnolongerservetoexpressorcarryouttheideasofitsbestpractitioners.

【目录】

Preface
Acknowledgments
UsingThisBook
PARTI:EXAMPLESOFVARIETIESANDMAPS
LECTURE1AffineandProjectiveVarieties
LECTURE2RegularFunctionsandMaps
LECTURE3Cones,Projections,andMoreAboutProducts
LECTURE4FamiliesandParameterSpaces
LECTURE5IdealsofVarieties,IrreducibleDecomposition,andtheNullstellensatz
LECTURE6GrassmanniansandRelatedVarieties
LECTURE7RationalFunctionsandRationalMaps
LECTURE8MoreExamples
LECTURE9DeterminantalVarieties
LECTURE10AlgebraicGroups

PARTII:ATTRIBUTESOFVARIETIES
LECTURE11DefinitionsofDimensionandElementaryExamples
LECTURE12MoreDimensionComputations
LECTURE13HilbertPolynomials
LECTURE14SmoothnessandTangentSpaces
LECTURE15GaussMaps,TangentialandDualVarieties
LECTURE16TangentSpacestoGrassmannians
LECTURE17FurtherTopicsInvolvingSmoothnessandTangentSpaces
LECTURE18Degree
LECTURE19FurtherExamplesandApplicationsofDegree
LECTURE20SingularPointsandTangentCones
LECTURE21ParameterSpacesandModuliSpaces
LECTURE22QuadricsHintsforSelectedExercises
References
Index