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 2
k ≤ 2
k' ≤ 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.
抄録全体を表示