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Line Bundles, Linear Systems, and Divisors

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

Abstract

We have already come across line bundles over curves: trivial, tangent, and cotangent bundles and their tensor powers. Thus, a natural question arises: given a curve, are there other line bundles over it? For instance, in the case of elliptic curves, all line bundles mentioned above are trivial, so this question means, in particular, whether there are nontrivial line bundles over a given elliptic 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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