| Project/Area Number |
22340009
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| Research Category |
Grant-in-Aid for Scientific Research (B)
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| Allocation Type | Single-year Grants |
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| Section | 一般 |
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| Research Field |
Algebra
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| Research Institution | Osaka University |
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Principal Investigator |
OGUISO Keiji 大阪大学, 理学(系)研究科(研究院), 教授 (40224133)
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| Co-Investigator(Kenkyū-buntansha) |
KONNO Kazuhiro 大阪大学, 大学院理学研究科, 教授 (10186869)
GOTO Ryuushi 大阪大学, 大学院理学研究科, 教授 (30252571)
TAKAHASHI Atsushi 大阪大学, 大学院理学研究科, 教授 (50314290)
SUMI Hiroki 大阪大学, 大学院理学研究科, 准教授 (40313324)
FUJIKI Akira 大阪大学, その他部局等, 名誉教授 (80027383)
USUI Sampei 大阪大学, その他部局等, 名誉教授 (90117002)
川口 周 大阪大学, 理学研究科, 准教授 (20324600)
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| Project Period (FY) |
2010-04-01 – 2015-03-31
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| Project Status |
Completed (Fiscal Year 2014)
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| Budget Amount *help |
¥12,480,000 (Direct Cost: ¥9,600,000、Indirect Cost: ¥2,880,000)
Fiscal Year 2014: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
Fiscal Year 2013: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2012: ¥4,550,000 (Direct Cost: ¥3,500,000、Indirect Cost: ¥1,050,000)
Fiscal Year 2011: ¥4,030,000 (Direct Cost: ¥3,100,000、Indirect Cost: ¥930,000)
Fiscal Year 2010: ¥1,690,000 (Direct Cost: ¥1,300,000、Indirect Cost: ¥390,000)
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| Keywords | 双有理変換 / 双正則変換 / エントロピー / ダイナミカル次数 / 有理多様体 / カラビ・ヤウ多様体 / ICM招待講演 / K3曲面 / 単有理多様体 / 超ケーラー多様体 / 自己同型 / クレモナ変換 / 錐予想 / 導来圏 / 超単純多様体 / コホモロジカル関手 |
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| Outline of Final Research Achievements |
Blending birational algebraic geometry and complex dynamics, I found, in my own works and my joint works, the first explicit examples of three dimensional rational manifolds and Calabi-Yau manifolds with biregular primitive automorphisms of positive entropy, a complete affirmative answer to the Kawamata-Morrison cone conjecture when the manifolds are Calabi-Yau manifolds of Wheler type, of any dimension, an affirmative answer to the Ueno (Ueno-Camapana) problem on the unirationality of certain threefolds of quotient type, a negative answer to the Gizatullin problem on the automorphisms of quartic K3 surfaces and the Cremona group of the ambient projectitive three space, as well as some new applications of complex dynamics to the liftability problem of automorphisms of K3 surfaces in positive characteristic. These works are highly estimated and I was elected an invited speaker of the Internatioal Congress of Mathematicians 2014 held at Seoul, Korea.
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