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Preliminaries

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

Abstract

The main focus of this course will be on complex algebraic curves, or, which is the same, Riemann surfaces. From the topological point of view, a Riemann surface is a two-dimensional oriented surface; its topological properties are uniquely determined by a nonnegative integer, the genus. At the same time, individual characteristics of algebraic curves are complicated, and two different curves, even of the same genus, usually bear little resemblance to each other. However, if we look at curves not one by one, but in families, it turns out that such families have a relatively simple structure and many remarkable properties, which find various applications in mathematics and theoretical physics. It is the transition from individual curves to families of curves that is the topic of the course.

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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