代数函数与Abelian函数导论

ChapterⅠTheRiemann-RochTheorem

1.LemmasonValuations

2.TheRiemann-RochTheorem

3.RemarksonDifferentialForms

4.ResiduesinPowerSeriesFields

5.TheSumoftheResidues

6.TheGenusFormulaofHurwitz

7.Examples

8.DifferentialsofSecondKind

9.FunctionFieldsandCurves

10.DivisorClasses

ChapterⅡTheFermatCurve

1.TheGenus

2.Differentials

3.RationalImagesoftheFermatCurve

4.DecompositionoftheDivisorClasses

ChapterⅢTheRiemannSurface

1.TopologyandAnalyticStructure

2.IntegrationontheRiemannSurface

ChapterⅣTheTheoremofAbel-Jacobi

1.AbelianIntegrals

2.AbelsTheorem

3.JacobisTheorem

4.RiemannsRelations

5.Duality

ChapterⅤPeriodsontheFermatCurve

1.TheLogarithmSymbol

2.PeriodsontheUniversalCoveringSpace

3.PeriodsontheFermatCurve

4.PeriodsontheRelatedCurves

ChapterⅥLinearTheoryofThetaFunctions

1.AssociatedLinearForms

2.DegenerateThetaFunctions

3.DimensionoftheSpaceofThetaFunctions

4.AbelianFunctionsandRiemann-RochTheoremontheToru

5.TranslationsofThetaFunctions

6.ProjectiveEmbedding

ChapterⅦHomomorphismsandDuality

1.TheComplexandRationalRepresentations

2.Rationalandp-adicRepresentations

3.Homomorphisms

4.CompleteReducibilityofPoincar

5.TheDualAbelianManifold

6.RelationswithThetaFunctions

7.TheKummerPairing

8.PeriodsandHomology

ChapterⅧRiemannMatricesandClassicalThetaFunctions

1.RiemannMatrices

2.TheSiegelUpperHalfSpace

3.FundamentalThetaFunctions

ChapterⅨ

InvolutionsandAbelianManifoldsofQuaternionType

1.Involutions

2.SpecialGnerators

3.Orders

4.LatticesandRiemannFormsonDeterminedbyQuaternionAlgebras

5.IsomorphismClasses

ChapteⅩ

ThetaFunctionsandDivisors

I.PositiveDivisors

2.ArbitraryDivisors

3.ExistenceofaRiemannFormonanAbelianVariety

Bibliography

Index

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