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代数幾何学セミナー
過去の記録 ～04/17｜次回の予定｜今後の予定 04/18～
| 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 |
2023年05月26日(金)
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
吉川 翔 氏 (東京工業大学, 理研)
Varieties in positive characteristic with numerically flat tangent bundle
吉川 翔 氏 (東京工業大学, 理研)
Varieties in positive characteristic with numerically flat tangent bundle
[ 講演概要 ]
The positivity condition imposed on the tangent bundle of a smooth projective variety is known to restrict the geometric structure of the variety. Demailly, Peternell and Schneider established a decomposition theorem for a smooth projective complex variety with nef tangent bundle. The theorem states that, up to an etale cover, such a variety has a smooth fibration admitting a smooth algebraic fiber space over an abelian variety whose fibers are Fano varieties, so one can say that such a variety decomposes into the "positive” part and the "flat” part. A positive characteristic analog of the above decomposition theorem was proved by Kanemitsu and Watanabe. The "flat” part of their theorem is a smooth projective variety with numerically flat tangent bundle. In this talk, I will introduce the result that every ordinary variety with numerically flat tangent bundle is an etale quotient of an ordinary Abelian variety. In particular, we obtain the decomposition theorem for Frobenius splitting varieties with nef tangent bundle. This talk is based on joint work with Sho Ejiri.
The positivity condition imposed on the tangent bundle of a smooth projective variety is known to restrict the geometric structure of the variety. Demailly, Peternell and Schneider established a decomposition theorem for a smooth projective complex variety with nef tangent bundle. The theorem states that, up to an etale cover, such a variety has a smooth fibration admitting a smooth algebraic fiber space over an abelian variety whose fibers are Fano varieties, so one can say that such a variety decomposes into the "positive” part and the "flat” part. A positive characteristic analog of the above decomposition theorem was proved by Kanemitsu and Watanabe. The "flat” part of their theorem is a smooth projective variety with numerically flat tangent bundle. In this talk, I will introduce the result that every ordinary variety with numerically flat tangent bundle is an etale quotient of an ordinary Abelian variety. In particular, we obtain the decomposition theorem for Frobenius splitting varieties with nef tangent bundle. This talk is based on joint work with Sho Ejiri.
