| Project/Area Number |
18K03231
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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 | Hokkaido University |
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Principal Investigator |
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| Project Period (FY) |
2018-04-01 – 2025-03-31
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| Project Status |
Completed (Fiscal Year 2024)
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| Budget Amount *help |
¥4,550,000 (Direct Cost: ¥3,500,000、Indirect Cost: ¥1,050,000)
Fiscal Year 2022: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
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: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2018: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
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| Keywords | シンプレクティック / ラグランジアン / 特異点 / 力学系 / ガロア理論 / 固定点 / 自己同型群 / 周期点 / 自己同型 / 離散力学系 / トレリ型定理 / カラビヤウ多様体 / シンプレクティック多様体 / アーベル多様体 |
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| Outline of Final Research Achievements |
We proved two results concerning primitive symplectic manifolds. First, we obtained a result on the structure of the nef cone, which is important for applying the global Torelli-type theorem. According to the minimal model theory, the nef cone is expected to be a mixture of two parts: a rational polyhedral part and a so-called circular part. However, we showed that in fact only one of these two parts appears; either the circular part or the rational polyhedral part, but not both. Moreover, we proved that primitive symplectic manifolds with such a nef cone form a dense subset in the moduli space. Second, we showed that the subset of primitive symplectic manifolds satisfying the abundance conjecture is open in the moduli space.
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| Academic Significance and Societal Importance of the Research Achievements |
特異点を持つシンプレクティック多様体に関しても非特異な場合と同じような結果が成立する可能性が示されたこと, および最近 EU で非特異とはかなり性質が異なるシンプレクティック多様体が構成されつつあることと合わせて, シンプレクティック多様体で非特異なものと共通な性質を持ちつつもこれまでと異なる幾何的な性質を持つものが存在する可能性があり, 他分野への影響を与える可能性もある.
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