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Compact Riemann Surfaces

In: Complex Analysis in One Variable

Author

Listed:
  • Raghavan Narasimhan

    (University of Chicago, Department of Mathematics)

  • Yves Nievergelt

    (Eastern Washington University, Department of Mathematics)

Abstract

In this chapter, we introduce Riemann surfaces and prove an important theorem which asserts that meromorphic functions on a compact Riemann surface form an algebraic function field in one variable (see §6). The chapter is meant to serve as an introduction to some tools which have proved to be very useful in several branches of mathematics, in particular, in several complex variables and algebraic geometry.

Suggested Citation

  • Raghavan Narasimhan & Yves Nievergelt, 2001. "Compact Riemann Surfaces," Springer Books, in: Complex Analysis in One Variable, edition 0, chapter 0, pages 161-185, Springer.
    • Handle: RePEc:spr:sprchp:978-1-4612-0175-5_9
    DOI: 10.1007/978-1-4612-0175-5_9
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