F-singularities and singularities in birational geometry in characteristic zero(Fostering Joint International Research)
| Project/Area Number |
15KK0152
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| Research Category |
Fund for the Promotion of Joint International Research (Fostering Joint International Research)
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| Allocation Type | Multi-year Fund |
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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, 教授 (40380670)
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| Research Collaborator |
TANAKA Hiromu 東京大学, 大学院数理科学研究科, 准教授 (50724514)
Cascini Paolo Imperial College London, Department of Mathematics, 教授
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| Project Period (FY) |
2016 – 2018
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| Project Status |
Completed (Fiscal Year 2018)
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| Budget Amount *help |
¥11,310,000 (Direct Cost: ¥8,700,000、Indirect Cost: ¥2,610,000)
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| Keywords | F特異点 / 大域的F正則多様体 / Fano型多様体 / 判定イデアル / 数値的Q-Gorenstein / 代数幾何学 / F正則特異点 / 特異点の変形 / 対数的Fano多様体 / 正標数 / WO有理特異点 |
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| Outline of Final Research Achievements |
A projective variety over an algebraically closed field of characteristic zero is said to be of globally F-regular type if its modulo p reduction is globally F-regular for almost all p. In joint work with Paolo Cascini, we discuss a conjecture of Karl Schwede and Karen Smith, which says that a projective variety of globally F-regular type is of Fano type. In particular, we prove that their conjecture holds if the variety is a 3-dimensional smooth projective variety with nef anti-canonical divisor.
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| Academic Significance and Societal Importance of the Research Achievements |
Schwede・Smithの予想はF特異点論と双有理幾何学を結びつける重要な予想であり、この予想が肯定的に解決されれば、F特異点論を用いたFano型多様体の研究が可能になる。Schwede・Smithの予想は2次元の場合に正しいことが知られていたが、高次元の場合についてはほとんど何もわかっていなかった。今回初めて3次元の結果が得られたが、これをきっかけに高次元の研究が加速することが期待される。
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Report
(4 results)
Research Products
(13 results)
