Arithmetic Study of Calabi-Yau threefolds
| Project/Area Number |
15K04771
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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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| Research Field |
Algebra
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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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| Research Collaborator |
YUI Noriko クイーンズ大学, 数理科学研究科, 教授
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| Project Period (FY) |
2015-04-01 – 2018-03-31
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| Project Status |
Completed (Fiscal Year 2017)
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| Budget Amount *help |
¥4,160,000 (Direct Cost: ¥3,200,000、Indirect Cost: ¥960,000)
Fiscal Year 2017: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
Fiscal Year 2016: ¥1,560,000 (Direct Cost: ¥1,200,000、Indirect Cost: ¥360,000)
Fiscal Year 2015: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
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| Keywords | ３次元カラビ・ヤウ多様体 / 形式群 / 数論幾何 / デルサルト型多様体 / ミラー対称性 / 国際研究者交流（カナダ） / 3次元カラビ・ヤウ多様体 / ミラー対称 / 国際研究者交流 / カラビ・ヤウ多様体 |
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| Outline of Final Research Achievements |
We studied the arithmetic of Calabi-Yau threefolds defined over a field of positive characteristic by placing a focus on their formal groups. The main objects of our study are weighted Delsarte threefolds and Calabi-Yau threefolds of Borcea-Voisin type. For such threefolds, we obtained a lot of new numerical data about the height of their formal groups and described relationships between the height of formal groups and several geometric properties of Calabi-Yau threefolds, such as the Hodge numbers. As an application, we investigated the formal groups of Calabi-Yau threefolds relating each other by mirror symmetry.
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Report
(4 results)
Research Products
(11 results)
