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 RiemannRoch 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.


Riemann Surface Meromorphic Function Compact Riemann Surface Weierstrass Point Jacobian Variety 
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Copyright information

© Springer Science+Business Media New York 1980

Authors and Affiliations

  • Hershel M. Farkas
    • 1
  • Irwin Kra
    • 2
  1. 1.Department of MathematicsThe Hebrew University of JerusalemJerusalemIsrael
  2. 2.Department of MathematicsS.U.N.Y. at Stony BrookStony BrookUSA

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