Compact Riemann Surfaces

  • Hershel M. Farkas
  • Irwin Kra
Part of the Graduate Texts in Mathematics book series (GTM, volume 71)


This is one of the two most important chapters of this book. In it, we prove (based on the existence theorems of the previous chapter) the three most important theorems concerning compact Riemann surfaces: the Riemann-Roch theorem, Abel’s theorem, and the Jacobi inversion theorem. Many applications of these theorems are obtained; and the simplest compact Riemann surfaces, the hyperelliptic ones, are discussed in great detail.


Filtration Manifold Assure Dition Dinates 


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Copyright information

© Springer Science+Business Media New York 1992

Authors and Affiliations

  • Hershel M. Farkas
    • 1
  • Irwin Kra
    • 2
  1. 1.Department of MathematicsHebrew UniversityJerusalemIsrael
  2. 2.Department of MathematicsState University of New YorkStony BrookUSA

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