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Complex Structure and the Topology of Curves

  • Maxim E. Kazaryan
  • Sergei K. Lando
  • Victor V. Prasolov
Chapter
Part of the Moscow Lectures book series (ML, volume 2)

Abstract

Every complex algebraic curve is a two-dimensional oriented surface. As we already know, the topology of such surfaces is very simple: for a compact surface, the topology is uniquely determined by its genus (or, equivalently, its Euler characteristic). However, along with a topological structure, a curve has a complex structure. It singles out analytic functions among all the functions on the curve.

Copyright information

© Springer Nature Switzerland AG 2018

Authors and Affiliations

  • Maxim E. Kazaryan
    • 1
  • Sergei K. Lando
    • 2
  • Victor V. Prasolov
    • 3
  1. 1.Steklov Mathematical Institute of RASNational Research University Higher School of Economics, Skolkovo Institute of Science and TechnologyMoscowRussia
  2. 2.National Research University Higher School of Economics, Skolkovo Institute of Science and TechnologyMoscowRussia
  3. 3.Independent University of MoscowMoscowRussia

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