Abstract
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.
Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
