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The monoid of effective divisor classes on a complex torus

Part of the Lecture Notes in Mathematics book series (LNM,volume 862)

Abstract

The Monoid M(X) of homology classes of effective cycles of codimension 1 on an n-dimensional complex torus X is characterized in terms of 2n × 2n integer matrices. Examples of tori X are constructed for which M(X) is finitely generated, as well as examples for which finite generation fails. In particular, it is shown that for "general" products X of elliptic curves, M(X) is finitely generated, while for Abelian varieties of the singular type, finite generation of the monoid fails.

Keywords

  • Elliptic Curve
  • Elliptic Curf
  • Theta Function
  • Abelian Variety
  • Chern Class

These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Partially supported by Illinois State University re-assigned research time.

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© 1981 Springer-Verlag

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Rosoff, J.A. (1981). The monoid of effective divisor classes on a complex torus. In: Libgober, A., Wagreich, P. (eds) Algebraic Geometry. Lecture Notes in Mathematics, vol 862. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0090893

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  • DOI: https://doi.org/10.1007/BFb0090893

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-10833-7

  • Online ISBN: 978-3-540-38720-6

  • eBook Packages: Springer Book Archive