| Project/Area Number |
19K14509
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| Research Category |
Grant-in-Aid for Early-Career Scientists
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| Allocation Type | Multi-year Fund |
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| Review Section |
Basic Section 11010:Algebra-related
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| Research Institution | Kobe University |
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Principal Investigator |
Sano Taro 神戸大学, 理学研究科, 准教授 (10773195)
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| Project Period (FY) |
2019-04-01 – 2024-03-31
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| Project Status |
Completed (Fiscal Year 2023)
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| Budget Amount *help |
¥3,640,000 (Direct Cost: ¥2,800,000、Indirect Cost: ¥840,000)
Fiscal Year 2022: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000)
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: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
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| Keywords | Fano多様体 / Calabi-Yau多様体 / 代数幾何学 / 変形理論 |
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| Outline of Research at the Start |
Fano 多様体, Calabi-Yau 多様体は代数多様体の分類において核となる対象である. 代数多様体の変形は分類を考える上での基本的操作である. 本研究の目的はCY多様体, およびFano 多様体の分類に進展をもたらすことである. 具体的には, 重要な未解決問題``3次元CY 多様体の有界性問題", ``Q-Fano 3-fold の数値的不変量の明示的評価", ``4 次元Fano多様体の分類" などに取り組む.
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| Outline of Final Research Achievements |
In joint work with Hashimoto, we constructed examples of non-Kahler Calabi-Yau 3-folds with arbitrarily large 2nd Betti numbers. I also constructed such examples in any dimension >3. We also computed their algebraic dimensions. Moreover, I proved the birational boundedness of K3 surfaces and Abelian surfaces which can appear as boundaries of 3-fold plt CY pairs.
In joint work with Tasin, we proved that most of Fano weighted hypersurfaces (of index 1) are K-stable. As an application, in joint work with Liu and Tasin, we constructed infinitely many families of Sasaki-Einstein metrics on odd-dimensional spheres.
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| Academic Significance and Societal Importance of the Research Achievements |
ケーラーでないカラビヤウ多様体の例の構成は代数幾何的手法に基づいて複素幾何的に興味深い例の構成に成功しており、広く興味深いと思われる。また、双有理有界性を証明したK3曲面やAbel曲面は長年研究がなされてきた対象であり、学術的に一定の価値がある。
また、Liu氏、Tasin氏との共同研究では代数的な手法を使って微分幾何学の長年の予想を解決した研究として、学術的価値は高いと思われる。
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