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manuscripta mathematica

, Volume 41, Issue 1–3, pp 45–74 | Cite as

Picard-Zahlen komplexer Tori

  • Erich Selder
Article

Abstract

We give explicit equations for the calculation of Chern classes of holomorphic line bundles on a complex torus X. As easy applications we deduce properties of the Picard numbers ρ(X) of n-dimensional tori, when the complex structure changes. The tori with ρ(X)≥k form a countable union of analytic subsets in a moduli space M; furthermore the set of tori with ρ(X)=k is empty or dense in M. For n-dimensional tori one has O≤ρ(X)≤n2, but for n≥3 not all numbers 0≤k≤n2 occur as Picard numbers. We conclude our considerations with a list of examples and with some remarks about this gap phenomenon in the distribution of Picard numbers of complex tori.

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Literatur

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    KODAIRA, K.; SPENCER, D.C.: On deformations of complex analytic structures, I, II; Ann. Math.67, 328–401, 403–465 (1958)Google Scholar
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Copyright information

© Springer-Verlag 1983

Authors and Affiliations

  • Erich Selder
    • 1
  1. 1.Fachbereich 6, MathematikUniversität OsnabrückOsnabrück

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