Various problems related to the classification in higher dimensional birational geometry
| Project/Area Number |
25287005
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| Research Category |
Grant-in-Aid for Scientific Research (B)
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| Allocation Type | Partial Multi-year Fund |
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| Section | 一般 |
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| Research Field |
Algebra
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| Research Institution | Kyoto University |
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Principal Investigator |
Mori Shigefumi 京都大学, 高等研究院, 特別教授 (00093328)
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| Research Collaborator |
Prokhorov Yuri ステクロフ研究所, 教授
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| Project Period (FY) |
2013-04-01 – 2018-03-31
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| Project Status |
Completed (Fiscal Year 2017)
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| Budget Amount *help |
¥7,670,000 (Direct Cost: ¥5,900,000、Indirect Cost: ¥1,770,000)
Fiscal Year 2017: ¥1,560,000 (Direct Cost: ¥1,200,000、Indirect Cost: ¥360,000)
Fiscal Year 2016: ¥1,560,000 (Direct Cost: ¥1,200,000、Indirect Cost: ¥360,000)
Fiscal Year 2015: ¥1,560,000 (Direct Cost: ¥1,200,000、Indirect Cost: ¥360,000)
Fiscal Year 2014: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
Fiscal Year 2013: ¥1,690,000 (Direct Cost: ¥1,300,000、Indirect Cost: ¥390,000)
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| Keywords | Qコニック束 / 因子収縮射 / フリップ収縮射 / 反標準線形系 / Du Val特異点 / 端末特異点 / Qデルペゾ束 / 極小モデルプログラム / 端収縮射 / フリップ / ファノ多様体 |
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| Outline of Final Research Achievements |
We study extremal contraction morphisms f to S of a terminal threefold X such that the inverse image F of a point s is a curve, and try to classify the neighbourhood of F especially when F is irreducible. They consist of three kinds, flipping contractions, divisorial contractions, and Q-conic bundles. Among them, flipping contractions were classified, and the other two kinds are studied. There are at most two non-Gorenstein points on F, and the classification of the case of one non-Gorenstein point has been completed.
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Report
(6 results)
Research Products
(14 results)
