代数幾何学セミナー
過去の記録 ~10/06|次回の予定|今後の予定 10/07~
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 |
2019年05月22日(水)
15:30-17:00 数理科学研究科棟(駒場) 122号室
河上 龍郎 氏 (東大数理)
Bogomolov type vanishing on three-dimensional Mori fiber spaces in positive characteristic
河上 龍郎 氏 (東大数理)
Bogomolov type vanishing on three-dimensional Mori fiber spaces in positive characteristic
[ 講演概要 ]
In characteristic zero, cotangent bundle of n(>1)-dimensional smooth projective varieties does not contain a big line bundle. This is a part of Bogomolov vanishing and this vanishing plays an important role in the proof of Miyaoka-Yau inequality. In positive characteristic, it is known that Bogomolov vanishing does not hold. There exists a general type surface whose cotangent bundle contains an ample line bundle. So, it is natural to ask when Bogomolov type vanishing holds in positive characteristic. In this talk, I discuss Bogomolov type vanishing on three-dimensional Mori fiber spaces in positive characteristic.
In characteristic zero, cotangent bundle of n(>1)-dimensional smooth projective varieties does not contain a big line bundle. This is a part of Bogomolov vanishing and this vanishing plays an important role in the proof of Miyaoka-Yau inequality. In positive characteristic, it is known that Bogomolov vanishing does not hold. There exists a general type surface whose cotangent bundle contains an ample line bundle. So, it is natural to ask when Bogomolov type vanishing holds in positive characteristic. In this talk, I discuss Bogomolov type vanishing on three-dimensional Mori fiber spaces in positive characteristic.