《复代数曲面》由世界图书出版公司出版。 |
1 introductionandbackground 1.1 abriefhistoryofalgebraiccurves 1.2 relationshipwithotherpartsofmathematics 1.2.1 numbertheory 1.2.2 singularitiesandthetheoryofknots 1.2.3 complexanalysis 1.2.4 abelianintegrals 1.3 realalgebraiccurves 1.3.1 hilbert'snullstellensatz 1.3.2 techniquesfordrawingrealalgebraiccurves 1.3.3 realalgebraiccurvesinsidecomplexalgebraiccurves 1.3.4 importantexamplesofrealalgebraiccurves 2 foundations 2.1 complexalgebraiccurvesincs 2.2 complexprojectivespaces 2.3 complexprojectivecurvesinps 2.4 affineandprojectivecurves 2.5 exercises 3 algebraicproperties .3.1 bezout'stheorem 3.2 pointsofinflectionandcubiccurves 3.3 exercises 4 topologicalproperties 4.1 thedegree-genusformula 4.1.1 thefirstmethodofproof 4.1.2 thesecondmethodofproof 4.2 branchedcoversofpi 4.3 proofofthedegree-genusformula 4.4 exercises 5 riemannsurfaces 5.1 theweierstrassfunction 5.2 riemannsurfaces 5.3 exercises 6 differentialsonriemannsurfaces 6.1 holomorphicdifferentials 6.2 abel'stheorem 6.3 theriemann-rochtheorem 6.4 exercises 7 singularcurves 7.1 resolutionofsingularities 7.2 newtonpolygonsandpuiseuxexpansions 7.3 thetopologyofsingularcurves 7.4 exercises aalgebra bcomplexanalysis ctopology c.1coveringprojections c.2thegenusisatopologicalinvariant c.3sphereswithhandles |
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