抄録
Gherardelli and Andreotti defined a quasi-abelian variety of kind k. However, this definition is somewhat vague and we do not know the real meaning of the ‘kind’. We give an example of a quasi-abelian variety which is of kind k › 0 but not of kind 0, in the sense of Gherardelli and Andreotti. We prove that if a quasi-abelian variety X = Cn / Γ has an ample Riemann form of kind k, then it has an ample Riemann form of kind k' for any k' with 2k ≤ 2k' ≤ n - m, where rank Γ = n + m. Next we consider the pair (X , L) of a quasi-abelian variety X and a positive line bundle L on it. We characterize an extendable line bundle L to a compactification $\\overline X$ of X.
