| Project/Area Number |
18K03216
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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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| Review Section |
Basic Section 11010:Algebra-related
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| Research Institution | Saga University |
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Principal Investigator |
Okada Takuzo 佐賀大学, 理工学部, 教授 (20547012)
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| Project Period (FY) |
2018-04-01 – 2023-03-31
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| Project Status |
Completed (Fiscal Year 2022)
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| Budget Amount *help |
¥4,290,000 (Direct Cost: ¥3,300,000、Indirect Cost: ¥990,000)
Fiscal Year 2021: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2020: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2019: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
Fiscal Year 2018: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
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| Keywords | ファノ多様体 / del Pezzo曲面束 / 双有理剛性 / 有理性問題 / K安定性 / del Pezzo束 |
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| Outline of Final Research Achievements |
We study del Pezzo fibrations of degree 1 over the projective line with terminal cyclic quotient singular points of type 1/2(1,1,1), and give a non-trivial sufficient condition for them to be birationally rigid. In particular, we show that birationally rigidity can be characterized by the K-condition for del Pezzo fibrations with 1/2(1,1,1) points which are embedded into a toric P(1,1,2,3)-bundle over the projective line. Moreover, we proved birational superrigidity for some codimension 4 prime Fano 3-folds, stable irrationality of many Fano varieties, and K-stability of many Fano 3-fold weighted complete intersections.
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| Academic Significance and Societal Importance of the Research Achievements |
代数多様体の有理性を判定する有理性問題は，代数幾何学において古くから研究されている重要問題である。特異点を持つdel Pezzo曲面束の有理性判定については多くのことが知られていない状況であった。del Pezzo曲面束が双有理剛的であれば非有理的であるため，本研究成果は，3次元del Pezzo 曲面束の有理性問題を着実に進展させたと言える。また，その他の結果も同様に，代数多様体の有理性問題や，3次元ファノ多様体のK安定性の研究を進展させた。
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