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


In this chapter we give applications and examples of the theory developed in the preceding chapters. The examples will consist mainly of taking concrete representations of compact Riemann surfaces given by algebraic functions, and computing on these surfaces various objects of interest. The applications will give rise to new characterizations of surfaces with some given property. The format of this chapter will differ considerably from the format of the preceding ones. Many details will be omitted. One of the aims of this chapter is to convince the reader that computations are quite often possible; and these computations yield beautiful results.


Riemann Surface Base Point Quadratic Differential Compact Riemann Surface Weierstrass Point 


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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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