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代数幾何学セミナー
過去の記録 ～04/23｜次回の予定｜今後の予定 04/24～
| 開催情報 | 金曜日 13:30～15:00 数理科学研究科棟(駒場) ハイブリッド開催/117号室 |
|---|---|
| 担当者 | 權業 善範、中村 勇哉、田中 公 |
2016年05月24日(火)
15:30-17:00 数理科学研究科棟(駒場) 122号室
山ノ井克俊 氏 (大阪大学)
ON PSEUDO KOBAYASHI HYPERBOLICITY OF SUBVARIETIES OF ABELIAN VARIETIES
(tba)
山ノ井克俊 氏 (大阪大学)
ON PSEUDO KOBAYASHI HYPERBOLICITY OF SUBVARIETIES OF ABELIAN VARIETIES
(tba)
[ 講演概要 ]
We prove that the Kobayashi pseudo distance of a closed subvariety X of an abelian variety A is a true distance outside the special set Sp(X) of X, where Sp(X) is the union of all positive dimensional translated abelian subvarieties of A which are contained in X. More strongly, we prove that a closed subvariety X of an abelian variety is taut modulo Sp(X); Every sequence fn : D → X of holomorphic mappings from the unit disc D admits a subsequence which converges locally uniformly, unless the image fn(K) of a fixed compact set K of D eventually gets arbitrarily close to Sp(X) as n gets larger. These generalize a classical theorem on algebraic degeneracy of entire holomorphic curves in irregular varieties.
We prove that the Kobayashi pseudo distance of a closed subvariety X of an abelian variety A is a true distance outside the special set Sp(X) of X, where Sp(X) is the union of all positive dimensional translated abelian subvarieties of A which are contained in X. More strongly, we prove that a closed subvariety X of an abelian variety is taut modulo Sp(X); Every sequence fn : D → X of holomorphic mappings from the unit disc D admits a subsequence which converges locally uniformly, unless the image fn(K) of a fixed compact set K of D eventually gets arbitrarily close to Sp(X) as n gets larger. These generalize a classical theorem on algebraic degeneracy of entire holomorphic curves in irregular varieties.
