| Project/Area Number |
18K13388
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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 | Osaka University |
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Principal Investigator |
Fujita Kento 大阪大学, 大学院理学研究科, 准教授 (40779146)
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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 |
¥4,160,000 (Direct Cost: ¥3,200,000、Indirect Cost: ¥960,000)
Fiscal Year 2021: ¥650,000 (Direct Cost: ¥500,000、Indirect Cost: ¥150,000)
Fiscal Year 2020: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2019: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
Fiscal Year 2018: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
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| Keywords | K安定性 / 極小モデル理論 / Fano多様体 / ファノ多様体 |
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| Outline of Final Research Achievements |
I considered K-stability of polarized varieties, especially of Fano varieties, from the viewpoint of birational geometry, e.g., minimal model program. We already have a valuative criterion for K-stability of Fano varieties, and recently Abban-Zhuang introduced a strong theory to test K-stability of Fano varieties. Using those valuative-type criteria and so on, together with Araujo, Castravet, Cheltsov, Kaloghiros, Martinez-Garcia, Shramov, Suess, Viswanathan, we could completely check whether a general member of each class of smooth Fano threefold is K-stable or not. Our result will be published as a forthcoming book.
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| Academic Significance and Societal Importance of the Research Achievements |
与えられたファノ多様体にいつケーラー・アインシュタイン計量が存在するかどうかを決定するのはカラビの問題と呼ばれ、これまで非常に難しいとされた。近年この問題はK安定性なる代数的条件と同値であることが証明されたが、それでもなお具体的なファノ多様体がいつK安定かどうか判定することは困難であった。付値判定法やAbban-Zhuangの理論の発展やそれらを組み合わせた公式を導出し、一般元という条件付きだが3次元でのカラビの問題を解決できたのは学術的意義は大きい。また本として出版する予定なので、理論の編纂は社会的意義も大きい。
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