| Project/Area Number |
18K03200
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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 of Education |
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Principal Investigator |
GOTO Yasuhiro 北海道教育大学, 教育学部, 教授 (40312425)
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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 |
¥3,770,000 (Direct Cost: ¥2,900,000、Indirect Cost: ¥870,000)
Fiscal Year 2020: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
Fiscal Year 2019: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
Fiscal Year 2018: ¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000)
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| Keywords | 数論的代数幾何 / 形式群 / カラビ・ヤウ多様体 / デルサルト型多様体 / ファイブレーション / 国際研究者交流 / 数論幾何 / 国際研究者交流（カナダ） / 楕円型ファイブレーション |
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| Outline of Final Research Achievements |
The formal groups of Calabi-Yau threeforlds with K3 or elliptic fibrations are considered. The relationship between the formal group of a threefold and those of its fibers were investigated, and in various special cases, the relationship of the formal groups was formulated explicitly. For threefolds of Delsarte type or of Borcea-Voisin type, the height of the formal groups was computed and the range of distribution of the values was determined. Similar calculations were done also on Calabi-Yau fourfolds of Delsarte type. In addition, an international workshop on Calabi-Yau varieties was organized every year.
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| Academic Significance and Societal Importance of the Research Achievements |
本研究は、各種ファイブレーションを持つ３次元カラビ・ヤウ多様体について、本体とファイバー間の形式群の関係性を調べた点で意義がある。これは、楕円曲線の形式群の変形を通して楕円型K3曲面の形式群を調べたArtinの研究の３次元化に向けた試みである。また、形式群の高さの計算を進め、３次元カラビ・ヤウ多様体の場合にその値分布を示すデータを更新し、４次元カラビ・ヤウ多様体においては高さの数値的データを得たことが新しい。
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