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Homogeneous line bundles over a toroidal group

Published online by Cambridge University Press:  22 January 2016

Yukitaka Abe
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A connected complex Lie group without non-constant holomorphic functions is called a toroidal group ([5]) or an (H, C)-group ([9]). Let X be an n-dimensional toroidal group. Since a toroidal group is commutative ([5], [9] and [10]), X is isomorphic to the quotient group Cn/Γ by a lattice of Cn. A complex torus is a compact toroidal group. Cousin first studied a non-compact toroidal group ([2]).

Let L be a holomorphic line bundle over X. L is said to be homogeneous if is isomorphic to L for all x ε X, where Tx is the translation defined by x ε X. It is well-known that if X is a complex torus, then the following assertions are equivalent:

Type
Research Article
Information
Nagoya Mathematical Journal , Volume 116 , December 1989 , pp. 17 - 24
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 1989

References

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