manuscripta mathematica

, Volume 41, Issue 1–3, pp 217–232 | Cite as

Two remarks concerning toroidal groups

  • Christian Vogt


This paper deals with two quite unrelated properties of toroidal groups. After some preliminary remarks in section 0, we calculate in section 1 the Dolbeault cohomology groups of a toroidal group under an additional assumption which assures that those are at least finite-dimensional. In particular, we obtain a Hodge decomposition for these special toroidal groups. In section 2, we first give a new proof of a theorem of Cousin concerning the sections of topologically trivial line bundles on toroidal groups. As an application, we then show that, in a sense to be made precise, most abelian complex Lie groups of dimension ≥2 do not have any hypersurfaces.


Line Bundle Number Theory Algebraic Geometry Additional Assumption Topological Group 
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Copyright information

© Springer-Verlag 1983

Authors and Affiliations

  • Christian Vogt
    • 1
  1. 1.Mathematisches InstitutUniversität DüsseldorfDüsseldorf 1Federal Republic of Germany

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