复代数曲线：Complex Algebraic Curves(London Mathematical Society Students Texts 23)

图书标准信息

• 作者 柯万（Kirwan.F.） 著
• 出版社 世界图书出版公司
• 出版时间 2008-05
• 版次 1
• ISBN 9787506292030
• 定价 29.00元
• 装帧 平装
• 开本 24开
• 纸张 其他
• 页数 264页
• 正文语种 英语
• 原版书名 complex algebraic curves

【内容简介】

Thisbookoncomplexalgebraiccurvesisintendedtobeaccessibletoanythirdyearmathematicsundergraduatewhohasattendedcoursesonalgebra，topologyandcomplexanalysis.ItisanexpandedversionofnoteswrittentoaccompanyalecturecoursegiventothirdyearundergraduatesatOxford.Ithasusuallybeenthecasethatanumberofgraduatestudentshavealsoattendedthecourse，andthelecturenoteshavebeenextendedsomewhatforthesakeofothersintheirposition.Howeverthisnewmaterialisnotintendedtodauntundergraduates，whocansafelyignoreit.TheoriginallecturecourseconsistedofChapters1to5（exceptforsomeof§3.1includingthedefinitionofintersectionmultiplicities）andpartofChapter6，althoughsomeofthecontentsofthesechapters（particularlytheintroductorymaterialinChapter1）wascoveredratherbriefly.

【作者简介】

Dame Frances Clare Kirwan, DBE FRS (born 1959) is a British mathematician, currently a Professor of Mathematics at the University of Oxford. Her fields of specialisation are algebraic and symplectic geometry.
http://en.wikipedia.org/wiki/Frances_Kirwan
https://www.maths.ox.ac.uk/people/profiles/frances.kirwan

【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