经典英文数学教材系列：代数曲线几何初步

图书标准信息

• 作者 [英]菌吉布森（Gibson C.G） 著
• 出版社 世界图书出版公司
• 出版时间 2009-01
• 版次 1
• ISBN 9787506292641
• 定价 35.00元
• 装帧 平装
• 开本 32开
• 纸张 胶版纸
• 页数 250页
• 正文语种 简体中文，英语

【内容简介】

　　GeneralBackgroundIfirstbecameinvolvedintheteachingofgeometryabouttwentyyearsago，whenmydepartmentintroducedanoptionalsecondyearcourseonthegeometryofplanecurves，partlytoredresstheimbalanceintheteachingofthesubject。ItWasmildlyrevolutionary，sinceitwentbacktoanearliersctofpreceptswherethedifferentialandalgebraicgeometryofcuweswerepursuedsimultaneously,totheirmutua！advantage.

【目录】

ListofIllustrations
ListofTables
Preface
1RealAlgebraicCurves
1.1ParametrizedandImplicitCurves
1.2IntroductoryExamples
1.3CurvesinPlanarKinematics

2GeneralGroundFields
2.1TwoMotivatingExamples
2.2Groups，RingsandFields
2.3GeneralAffinePlanesandCurves
2.4ZeroSetsofAlgebraicCurves

3PolynomialAlgebra
3.1FactorizationinDomains
3.2PolynomialsinOneVariable
3.3PolynomialsinSeveralVariables
3.4HomogeneousPolynomials
3.5FormalDifferentiation

4AtfineEquivalence
4.1AffineMaps
4.2AfflineEquivalentCurves
4.3DegreeasanAffineInvariant
4.4CentresasAffineInvariants

5AfflineConics
5.1AfflineClassification
5.2TheDeltaInvariants
5.3UniquenessofEquations

6SingularitiesofAflineCurves
6.1IntersectionNumbers
6.2MultiplicityofaPointonaCurve
6.3SingularPoints

7TangentstoAflineCurves
7.1GeneralitiesaboutTangents
7.2TangentsatSimplePoints
7.3TangentsatDoublePoints
7.4TangentsatPointsofHigherMultiplicity

8RationalAflineCurves
8.1RationalCurves
8.2DiophantineEquations
8.3ConicsandIntegrals

9ProjectiveAlgebraicCurves
9.1TheProjectivePlane
9.2ProjectiveLines
9.3AtfinePlanesintheProjectivePlane
9.4ProjectiveCurves
9.5AffineViewsofProjectiveCurves

10SingularitiesofProjectiveCurves
10.1IntersectionNumbers
10.2MultiplicityofaPointonaCurve
10.3SingularPoints
10.4DeltaInvariantsviewedProjectively

11ProjectiveEquivalence
11.1ProjectiveMaps
11.2ProjectiveEquivalence
11.3ProjectiveConics
11.4AflineandProjectiveEquivalence

12ProjectiveTangents
12.1TangentstoProjectiveCurves
12.2TangentsatSimplePoints
12.3CentresviewedProjectively
12.4FociviewedProjectively
12.5TangentsatSingularPoints
12.6Asymptotes

13Flexes
13.1HessianCurves
13.2ConfigurationsofFlexes

14IntersectionsofProiectiveCurves
14．1TheGeometricIdea
14．2ResultantsinOneVariable
14．3ResultantsinSevera!Variables
14．4B6zout’STheorem
14．5ThcMultiplicityInequality
14．6InvarianceoftheIntersectionNumber

15ProiectiveCubics
15．1GeometricTypes0fCubics
15．2CubicsofGeneralType
15．3SingularIrreducibleCubics
15．4ReducibleCubics

16LinearSystems
16．1ProjectiveSpacesofCurves
16．2PcncilsofCuiNes
16．3SolvingQuarticEquations
16．4SubspacesorProjectiveSpaces
16．5LinearSystemsofCulwes
16．6DualCulNes

17TheGroupStructureonaCubic
17．1TheNineAssociatedPoints
17．2TheStarOperation
17．3CubicsasGroups
17．4GroupComputations
17．5DeterminationoftheGroups

18RationalProjectiveCurves
18．1ThcProjectiveConcept
18．2QuarticswithThreeDoublePoints
18．3ThcDeficiencyofaCHIve
18．4SomeRationalCurves
18．5SomeNon-RationalCurves
Index