书籍详情
复代数曲面
作者：（英）柯万
出版社：世界图书出版公司
出版时间：2008-01-01
ISBN：9787506292030
定价：¥29.00
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内容简介
本书由世界图书出版公司北京公司和剑桥大学出版社合作出版。
作者简介
暂缺《复代数曲面》作者简介
目录
1Introductionandbackground
1.1Abriefhistoryofalgebraiccurves
1.2Relationshipwithotherpartsofmathematics
1.2.1Numbertheory
1.2.2Singularitiesandthetheoryofknots
1.2.3Complexanalysis
1.2.4Abelianintegrals
1.3RealAlgebraicCurves
1.3.1Hilbert'sNullstellensatz
1.3.2Techniquesfordrawingrealalgebraiccurves
1.3.3Realalgebraiccurvesinsidecomplexalgebraiccurves
1.3.4Importantexamplesofrealalgebraiccurves
2Foundations
2.1ComplexalgebraiccurvesinCs
2.2Complexprojectivespaces
2.3ComplexprojectivecurvesinPs
2.4Affineandprojectivecurves
2.5Exercises
3Algebraicproperties
3.1Bezout'stheorem
3.2Pointsofinflectionandcubiccurves
3.3Exercises
4Topologicalproperties
4.1Thedegree-genusformula
4.1.1Thefirstmethodofproof
4.1.2Thesecondmethodofproof
4.2BranchedcoversofPI
4.3Proofofthedegree-genusformula
4.4Exercises
5Riemannsurfaces
5.1TheWeierstrassfunction
5.2Riemannsurfaces
5.3Exercises
6DifferentialsonRiemannsurfaces
6.1Holomorphicdifferentials
6.2Abel'stheorem
6.3TheRiemann-Rochtheorem
6.4Exercises
7Singularcurves
7.1ResolutionofSingularities
7.2NewtonpolygonsandPuiseuxexpansions
7.3Thetopologyofsingularcurves
7.4Exercises
AAlgebra
BComplexanalysis
CTopology
C.1Coveringprojections
C.2Thegenusisatopologicalinvariant
C.3Sphereswithhandles
1.1Abriefhistoryofalgebraiccurves
1.2Relationshipwithotherpartsofmathematics
1.2.1Numbertheory
1.2.2Singularitiesandthetheoryofknots
1.2.3Complexanalysis
1.2.4Abelianintegrals
1.3RealAlgebraicCurves
1.3.1Hilbert'sNullstellensatz
1.3.2Techniquesfordrawingrealalgebraiccurves
1.3.3Realalgebraiccurvesinsidecomplexalgebraiccurves
1.3.4Importantexamplesofrealalgebraiccurves
2Foundations
2.1ComplexalgebraiccurvesinCs
2.2Complexprojectivespaces
2.3ComplexprojectivecurvesinPs
2.4Affineandprojectivecurves
2.5Exercises
3Algebraicproperties
3.1Bezout'stheorem
3.2Pointsofinflectionandcubiccurves
3.3Exercises
4Topologicalproperties
4.1Thedegree-genusformula
4.1.1Thefirstmethodofproof
4.1.2Thesecondmethodofproof
4.2BranchedcoversofPI
4.3Proofofthedegree-genusformula
4.4Exercises
5Riemannsurfaces
5.1TheWeierstrassfunction
5.2Riemannsurfaces
5.3Exercises
6DifferentialsonRiemannsurfaces
6.1Holomorphicdifferentials
6.2Abel'stheorem
6.3TheRiemann-Rochtheorem
6.4Exercises
7Singularcurves
7.1ResolutionofSingularities
7.2NewtonpolygonsandPuiseuxexpansions
7.3Thetopologyofsingularcurves
7.4Exercises
AAlgebra
BComplexanalysis
CTopology
C.1Coveringprojections
C.2Thegenusisatopologicalinvariant
C.3Sphereswithhandles
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