代数幾何学セミナー
過去の記録 ~10/09|次回の予定|今後の予定 10/10~
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 |
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担当者 | 權業 善範、中村 勇哉、田中 公 |
2012年06月25日(月)
15:30-17:00 数理科学研究科棟(駒場) 122号室
小木曽啓示 氏 (大阪大学)
Automorphism groups of Calabi-Yau manifolds of Picard number two (JAPANESE)
小木曽啓示 氏 (大阪大学)
Automorphism groups of Calabi-Yau manifolds of Picard number two (JAPANESE)
[ 講演概要 ]
We prove that the automorphism group of an odd dimensional Calabi-Yau manifold of Picard number two is always a finite group. This makes a sharp contrast to the automorphism groups of K3 surfaces and hyperk\\"ahler manifolds and birational automorphism groups, as I shall explain. We also clarify the relation between finiteness of the automorphism group (resp. birational automorphism group) and the rationality of the nef cone (resp. movable cone) for a hyperk\\"ahler manifold of Picard number two. We will also discuss a similar conjectual relation for a Calabi-Yau threefold of Picard number two, together with exsistence of rational curve, expected by the cone conjecture.
We prove that the automorphism group of an odd dimensional Calabi-Yau manifold of Picard number two is always a finite group. This makes a sharp contrast to the automorphism groups of K3 surfaces and hyperk\\"ahler manifolds and birational automorphism groups, as I shall explain. We also clarify the relation between finiteness of the automorphism group (resp. birational automorphism group) and the rationality of the nef cone (resp. movable cone) for a hyperk\\"ahler manifold of Picard number two. We will also discuss a similar conjectual relation for a Calabi-Yau threefold of Picard number two, together with exsistence of rational curve, expected by the cone conjecture.