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黎曼曲面2025|PDF|Epub|mobi|kindle电子书版本百度云盘下载

黎曼曲面
  • Farkas，H.M.编 著
  • 出版社： 北京;西安：世界图书出版公司
  • ISBN：7506259478
  • 出版时间：2003
  • 标注页数：363页
  • 文件大小：43MB
  • 文件页数：381页
  • 主题词：

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图书目录

CHAPTER 0 An Overview1

0.1．Topological Aspects,Uniformization,and Fuchsian Groups2

0.2．Algebraic Functions4

0.3．Abelian Varieties6

0.4．More Analytic Aspects7

CHAPTER Ⅰ Riemann Surfaces9

Ⅰ.1．Definitions and Examples9

Ⅰ.2．Topology of Riemann Surfaces13

Ⅰ.3．Differential Forms22

Ⅰ.4．Integration Formulae28

CHAPTER Ⅱ Existence Theorems32

Ⅱ.1．Hilbert Space Theory—A Quick Review32

Ⅱ.2．Weyl's Lemma33

Ⅱ.3．The Hilbert Space of Square Integrable Forms39

Ⅱ.4．Harmonic Differentials45

Ⅱ.5．Meromorphic Functions and Differentials50

CHAPTER Ⅲ Compact Riemann Surfaces54

Ⅲ.1．Intersection Theory on Compact Surfaces54

Ⅲ.2．Harmonic and Analytic Differentials on Compact Surfaces56

Ⅲ.3．Bilinear Relations64

Ⅲ.4．Divisors and the Riemann-Roch Theorem69

Ⅲ.5．Applications of the Riemann-Roch Theorem79

Ⅲ.6．Abel's Theorem and the Jacobi Inversion Problem91

Ⅲ.7．Hyperelliptic Riemann Surfaces99

Ⅲ.8．Special Divisors on Compact Surfaces109

Ⅲ.9．Multivalued Functions126

Ⅲ.10．Projective Imbeddings136

Ⅲ.11．More on the Jacobian Variety142

Ⅲ.12．Torelli's Theorem161

CHAPTER Ⅳ Uniformization166

Ⅳ.1．More on Harmonic Functions(A Quick Review)166

Ⅳ.2．Subharmonic Functions and Perron's Method171

Ⅳ.3．A Classification of Riemann Surfaces178

Ⅳ.4．The Uniformization Theorem for Simply Connected Surfaces194

Ⅳ.5．Uniformization of Arbitrary Riemann Surfaces203

Ⅳ.6．The Exceptional Riemann Surfaces207

Ⅳ.7．Two Problems on Moduli211

Ⅳ.8．Riemannian Metrics213

Ⅳ.9．Discontinuous Groups and Branched Coverings220

Ⅳ.10．Riemann-Roch—An Alternate Approach237

Ⅳ.11．Algebraic Function Fields in One Variable241

CHAPTER Ⅴ Automorphisms of Compact Surfaces-Elementary Theory257

Ⅴ.1．Hurwitz's Theorem257

Ⅴ.2．Representations of the Automorphism Group on Spaces of Differentials269

Ⅴ.3．Representation of Aut M on H1(M)286

Ⅴ.4．The Exceptional Riemann Surfaces293

CHAPTER Ⅵ Theta Functions298

Ⅵ1.1．The Riemann Theta Function298

Ⅵ.2．The Theta Functions Associated with a Riemann Surface304

Ⅵ.3．The Theta Divisor309

CHAPTER Ⅶ Examples321

Ⅶ.1．Hyperelliptic Surfaces (Once Again)321

Ⅶ.2．Relations Among Quadratic Differentials333

Ⅶ.3．Examples of Non-hyperelliptic Surfaces337

Ⅶ.4．Branch Points of Hyperelliptic Surfaces as Holomorphic Functions of the Periods348

Ⅶ.5．Examples of Prym Differentials350

Ⅶ.6．The Trisecant Formula351

Bibliography356

Index359

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