ON QUASI-ABELIAN VARIETIES OF KIND $ k $
スポンサーリンク
概要
- 論文の詳細を見る
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 = \mathbb{C}^n\Gamma $ has an ample Riemann form of kind $ k $, then it has an ample Riemann form of kind $ k' $ for any $ k' $ with $ 2k \leqq 2k' \leqq {n-m} $, where rank $ \Gamma = {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 $.
- Faculty of Mathematics, Kyushu Universityの論文
著者
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Abe Yukitaka
Departement De Mathematiques Universite De Toyama
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UMENO Takashi
Department of Mathematics Kyushu Sangyo University
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