《代数几何基培础教程》由J.Ha或模委到rris 编写，出版于2000-6-1。

• 书名 代数几何基础教程
• 别名 Algebraic Geometry A First Course
• 作者 J.Harris
• 出版社 世界图书出版公司
• 出版时间 2000年6月

图来自书简介

　　This book 比兵针坐维冷多is based on one-semester courses given at Harvard i养住测官益病或运刻证n 1984， at Brown in 1985， and at Harvard in 1988. It is intended to be， as the title suggests， a first introd与承uction to the sub360百科ject. Eve钢载站诉马宣办参缩置校n so， a few words are in order about the purposes of the book. Algebraic geometry h防as developed tremendously over the last century. During the 19th century， the subject was practiced on a relatively concrete， down-to-earth level; the main objects of study were projec零怕tive varieties， and the techniques for the most part were grounded in geo去女容补吸metric constructions. This approach flourished during the middle of the century and reached its culmin希势短划优ation in the wo层rk of the Italian school around the end of the 19th and t广门林湖改离书刑似面沉he beginning of th守叫破权道正迅龙e 20th centuries.Ultimately， the subject w家益延谓as pushed beyond the limits of its foundations: by the end of its period the Ita乎叫益翻土lian school had progressed to the point where the language and techniques of the subject could no longer serve to express or carry out the ideas of its 短语best practitioners.本书为英文版。

图书目录

　　Preface

　　Acknowledgment受科优s

　　UsingThisBook

　　PARTI:EXAMPLESOFVARIETIES乙西位夜茶青特取ANDMAPS

　　LECTURE1

　　AffineandProj袁看前前法指ectiveVarieties

　　ANoteAboutOurField

　　AffineSpaceandA束离构酸务医心参ffineVarieties

　　ProjectiveSpaceandProjectiveVarieties

　　LinearSpaces

　　FiniteSets

　　Hypersurfaces

　　AnalyticSubvarietiesandSubmanifolds

　　TheTwistedCubic

　　RationalNormalCurves

　　DeterminantalRepresentationoftheRationalNormalCurve

　　AnotherParametrizationoftheRationalNormalCurve

　　TheFamilyofPlaneConics

　　ASyntheticConstructionoftheRationalNormalCurve

　　OtherRationalCurves

　　VarietiesDefinedoverSubfieldsofK

　　ANoteonDimension,Smoothness,andDegree

　　LECTURE2

　　RegularFunctionsandMaps

　　TheZariskiTopology

　　RegularFunctionsonanAftineVariety

　　ProjectiveVarieties

　　RegularMaps

　　TheVeroneseMap

　　DeterminantalRepresentationofVeroneseVarieties

　　SubvarietiesofVeroneseVarieties

　　TheSegreMaps

　　SubvarietiesofSegreVarieties

　　ProductsofVarieties

　　Graphs

　　FiberProducts

　　CombinationsofVeroneseandSegreMaps

　　LECTURE3

　　Cones,Projections,andMoreAboutProducts

　　Cones

　　Quadrics

　　Projections

　　MoreCones

　　MoreProjections

　　ConstructibleSets

　　LECTURE4

　　FamiliesandParameterSpaces

　　FamiliesofVarieties

　　TheUniversalHyperplane

　　TheUniversalHyperplaneSection

　　ParameterSpacesofHypersurfaces

　　UniversalFamiliesofHypersurfaces

　　AFamilyofLines

　　LECTURE5

　　IdealsofVarieties,IrreducibleDecomposition,andtheNullstellensatz

　　GeneratingIdeals

　　IdealsofProjectiveVarieties

　　IrreducibleVarietiesandIrreducibleDecomposition

　　GeneralObjects

　　GeneralProjections

　　GeneralTwistedCubics

　　DoublePointLoci

　　ALittleAlgebra

　　RestatementsandCorollaries

　　LECTURE6

　　GrassmanniansandRelatedVarieties

　　Grassmannians

　　SubvarietiesofGrassmannians

　　TheGrassmannianG(1,3)

　　AnAnalogoftheVeroneseMap

　　IncidenceCorrespondences

　　VarietiesofIncidentPlanes

　　TheJoinofTwoVarieties

　　FanoVarieties

　　LECTURE7

　　RationalFunctionsandRationalMaps

　　RationalFunctions

　　RationalMaps

　　GraphsofRationalMaps

　　BirationalIsomorphism

　　TheQuadricSurface

　　Hypersurfaces

　　DegreeofaRationalMap

　　Blow-Ups

　　BlowingUpPoints

　　BlowingUpSubvarieties

　　TheQuadricSurfaceAgain

　　TheCubicScrollinP4

　　Unirationality

　　LECTURE8

　　MoreExamples

　　TheJoinofTwoVarieties

　　TheSecantPlaneMap

　　SecantVarieties

　　TrisecantLines,etc.

　　JoinsofCorrespondingPoints

　　RationalNormalScrolls

　　Higher-DimensionalScrolls

　　MoreIncidenceCorrespondences

　　FlagManifolds

　　MoreJoinsandIntersections

　　QuadricsofRank4

　　RationalNormalScrollsII

　　LECTURE9

　　DeterminantalVarieties

　　GenericDeterminantalVarieties

　　SegreVarieties

　　SecantVarietiesofSegreVarieties

　　LinearDeterminantalVarietiesinGeneral

　　RationalNormalCurves

　　SecantVarietiestoRationalNormalCurves

　　RationalNormalScrollsIII

　　RationalNormalScrollsIV

　　MoreGeneralDeterminantalVarieties

　　SymmetricandSkew-SymmetricDeterminantalVarieties

　　FanoVarietiesofDeterminantalVarieties

　　LECTURE10

　　AlgebraicGroups

　　TheGeneralLinearGroupGLnK

　　TheOrthogonalGroupSOnK

　　TheSymplecticGroupSp2nK

　　GroupActions

　　PGLn+1KactsonPn

　　PGL2KActsonP2

　　PGL2KActsonP3

　　PGL2KActsonPn

　　PGL3KActsonP5

　　PGL3KActsonP9

　　POnKActsonPn-1(automorphismsoftheGrassmannian)

　　PGLnKActsonP(∧kKn)

　　Quotients

　　QuotientsofAffineVarietiesbyFiniteGroups

　　QuotientsofAffineSpace

　　SymmetricProducts

　　QuotientsofProjectiveVarietiesbyFiniteGroups

　　WeightedProjectiveSpaces

　　PARTII:ATTRIBUTESOFVARIETIES

　　LECTURE11

　　DefinitionsofDimensionandElementaryExamples

　　Hypersurfaces

　　CompleteIntersections

　　ImmediateExamples

　　TheUniversalk-Plane

　　VarietiesofIncidentPlanes

　　SecantVarieties

　　SecantVarietiesinGeneral

　　JoinsofVarieties

　　FlagManifolds

　　(Some)SchubertVarieties

　　LECTURE12

　　MoreDimensionComputations

　　DeterminantalVarieties

　　FanoVarieties

　　ParameterSpacesofTwistedCubics

　　TwistedCubics

　　TwistedCubicsonaGeneralSurface

　　CompleteIntersections

　　CurvesofType(a,b)onaQuadric

　　DeterminantalVarieties

　　GroupActions

　　GL(V)ActsonSymdVand∧kV

　　PGLn+1KActson(Pn)landG(k,n)l

　　LECTURE13

　　HilbertPolynomials

　　HilbertFunctionsandPolynomials

　　HilbertFunctionoftheRationalNormalCurve

　　HilbertFunctionoftheVeroneseVariety

　　HilbertPolynomialsofCurves

　　Syzygies

　　ThreePointsinP2

　　FourPointsinP2

　　CompleteIntersections:KoszulComplexes

　　LECTURE14

　　SmoothnessandTangentSpaces

　　TheZariskiTangentSpacetoaVariety

　　ALocalCriterionforIsomorphism

　　ProjectiveTangentSpaces

　　DeterminantalVarieties

　　LECTURE15

　　GaussMaps,TangentialandDualVarieties

　　ANoteAboutCharacteristic

　　GaussMaps

　　TangentialVarieties

　　TheVarietyofTangentLines

　　JoinsofIntersectingVarieties

　　TheLocusofBitangentLines

　　DualVarieties

　　LECTURE16

　　TangentSpacestoGrassmannians

　　TangentSpacestoGrassmannians

　　TangentSpacestoIncidenceCorrespondences

　　VarietiesofIncidentPlanes

　　TheVarietyofSecantLines

　　VarietiesSweptoutbyLinearSpaces

　　TheResolutionoftheGenericDeterminantalVariety

　　TangentSpacestoDualVarieties

　　TangentSpacestoFangVarieties

　　LECTURE17

　　FurtherTopicsInvolvingSmoothnessandTangentSpaces

　　GaussMapsonCurves

　　OsculatingPlanesandAssociatedMaps

　　TheSecondFundamentalForm

　　TheLocusofTangentLinestoaVariety

　　Bertini'sTheorem

　　Blow-ups,NashBlow-ups,andtheResolutionofSingularities

　　SubadditivityofCodimensionsofIntersections

　　LECTURE18

　　Degree

　　Bezout'sTheorem

　　TheRationalNormalCurves

　　MoreExamplesofDegrees

　　VeroneseVarieties

　　SegreVarieties

　　DegreesofConesandProjections

　　JoinsofVarieties

　　UnirationalityofCubicHypersurfaces

　　LECTURE19

　　FurtherExamplesandApplicationsofDegree

　　MultidegreeofaSubvarietyofaProduct

　　ProjectiveDegreeofaMap

　　JoinsofCorrespondingPoints

　　VarietiesofMinimalDegree

　　DegreesofDeterminantalVarieties

　　DegreesofVarietiesSweptoutbyLinearSpaces

　　DegreesofSomeGrassmannians

　　Harnack'sTheorem

　　LECTURE20

　　SingularPointsandTangentCones

　　TangentCones

　　TangentConestoDeterminantalVarieties

　　Multiplicity

　　ExamplesofSingularities

　　ResolutionofSingularitiesforCurves

　　LECTURE21

　　ParameterSpacesandModuliSpaces

　　ParameterSpaces

　　ChowVarietSes

　　HilbertVarieties

　　CurvesofDegree2

　　ModuliSpaces

　　PlaneCubics

　　LECTURE22

　　Quadrics

　　GeneralitiesaboutQuadrics

　　TangentSpacestoQuadrics

　　PlaneConics

　　QuadricSurfaces

　　QuadficsinPn

　　LinearSpacesonQuadrics

　　LinesonQuadrics

　　PlanesonFour-DimensionalQuadrics

　　FanoVarietiesofQuadricsinGeneral

　　FamiliesofQuadrics

　　TheVarietyofQuadricsinP1

　　TheVarietyofQuadricsinP2

　　CompleteConics

　　QuadricsinPn

　　PencilsofQuadrics

　　HintsforSelectedExercises

　　References

　　Index