| Project/Area Number |
26400039
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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 | The University of Tokyo |
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Principal Investigator |
Takagi Shunsuke 東京大学, 大学院数理科学研究科, 准教授 (40380670)
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| Project Period (FY) |
2014-04-01 – 2017-03-31
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| Project Status |
Completed (Fiscal Year 2016)
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| Budget Amount *help |
¥4,810,000 (Direct Cost: ¥3,700,000、Indirect Cost: ¥1,110,000)
Fiscal Year 2016: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
Fiscal Year 2015: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
Fiscal Year 2014: ¥2,340,000 (Direct Cost: ¥1,800,000、Indirect Cost: ¥540,000)
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| Keywords | F特異点 / 可換環論 / 特異点論 / 局所コホモロジー / 代数幾何学 / 標準特異点 / 対数的端末特異点 / 一般超平面切断 / F正則特異点 / 乗数イデアル / 判定イデアル |
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| Outline of Final Research Achievements |
``F-singularities" are a generic term used to refer to singularities defined in terms of Frobenius maps, and there are four basic classes of F-singularities, F-regular, F-pure, F-rational and F-injective singularities. F-singularities are expected to correspond to the singularities in birational geometry in characteristic zero, and many researchers have studied this correspondence. In this research project, we obtained the following two results related to this correspondence: (1) When X is a numerically Q-Gorenstein variety over an algebraically closed field of characteristic zero, we proved that the multiplier ideals on X (in the sense of de Fernex-Hacon) coincide, after reduction to characteristic p>>0, with the test ideals. (2) We introduced a new class of F-singularities, F-nilpotent singularities, and gave a Hodge theoretic interpretation of (3-dimensional) F-nilpotent normal isolated singularities.
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