2018 Fiscal Year Final Research Report
On families of algebraic varieties admitting unipotent group actions from the viewpoint of Minimal Model Program
| Project/Area Number |
15K04805
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| Research Category |
Grant-in-Aid for Scientific Research (C)
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| Allocation Type | Multi-year Fund |
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| Section | 一般 |
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| Research Field |
Algebra
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| Research Institution | Saitama University |
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Principal Investigator |
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| Research Collaborator |
Adrien Dubouloz
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| Project Period (FY) |
2015-04-01 – 2019-03-31
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| Keywords | ユニポテント代数群 / シリンダー / 森ファイバー空間 / 極小モデル理論 |
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| Outline of Final Research Achievements |
We are interested in the following naturally looking problem "In which case, a given fibration between algebraic varieties whose general closed fibers admit effective unipotent group actions possesses an action the same group arising from those on general fibers ? ". This problem itself is quite difficult to accomplish completely, nevertheless we succeed into obtaining a certain sufficient condition. Meanwhile, by getting the above mentioned problem globalized, we consider the problem asking " Which kinds of Mori Fiber Spaces contain cylinders that are compatible with fiber structure ?" As for this problem, we know finally that the essence lies in behavior of the generic fibers, furthermore, we can obtain an effective criterion on the existence of cylinders depending on a given Mori Fiber Space.
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| Free Research Field |
代数幾何学
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| Academic Significance and Societal Importance of the Research Achievements |
本研究課題は純粋数学に関する研究に基づくものであるので，社会への直接的な貢献は見えづらく，主に研究代表者の知的好奇心により支えられている．しかし中長期的なスパンで見れば，代数幾何学の基礎研究は実生活への応用は起こり得る．(例えば代数曲線暗号理論はクレジットカードでネット経由で買い物をする時に本質的に役立っている．)
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