| Project/Area Number |
17K14156
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| Research Category |
Grant-in-Aid for Young Scientists (B)
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| Allocation Type | Multi-year Fund |
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| Research Field |
Algebra
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| Research Institution | The University of Tokyo |
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Principal Investigator |
Hashimoto Kenji 東京大学, 大学院数理科学研究科, 特任研究員 (00793986)
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| Project Period (FY) |
2017-04-01 – 2023-03-31
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| Project Status |
Completed (Fiscal Year 2022)
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| Budget Amount *help |
¥1,690,000 (Direct Cost: ¥1,300,000、Indirect Cost: ¥390,000)
Fiscal Year 2020: ¥390,000 (Direct Cost: ¥300,000、Indirect Cost: ¥90,000)
Fiscal Year 2019: ¥390,000 (Direct Cost: ¥300,000、Indirect Cost: ¥90,000)
Fiscal Year 2018: ¥390,000 (Direct Cost: ¥300,000、Indirect Cost: ¥90,000)
Fiscal Year 2017: ¥520,000 (Direct Cost: ¥400,000、Indirect Cost: ¥120,000)
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| Keywords | K3曲面 / 格子理論 / 自己同型 / 有限群 / 無限群 / 保型形式 / ミラー対称性 / 代数幾何 / クレモナ変換 / カラビ・ヤウ多様体 / 格子 |
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| Outline of Final Research Achievements |
K3 surfaces are important objects in various branches of mathematics. In this research we work over the complex numbers and they are 4-dimensional spaces in the ordinary meaning. One of our main interests is symmetry. In other words, we did the very detailed research on a "special" kind of K3 surfaces, in the same sense that equilateral triangles are special. In particular, we study K3 surfaces with higher symmetry; or determine the symmetry under some conditions (lower Picard numbers, and so on). In addition, we studied "periods" of K3 surfaces, which are important in the study of K3 surfaces. We observed the relation between these periods and so-called automorphic forms, and obtained concrete results. This is considered as a geometric approach to study automorphic forms.
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| Academic Significance and Societal Importance of the Research Achievements |
K3曲面は数学において重要かつ基本的な研究対象と考えられる。従って、様々な場面でK3曲面の知識（情報）が必要あるいは有用となる。例えば、数学においてのみならず数理物理学でも重要であるカラビ・ヤウ3次元多様体の研究において、その2次元版と考えられるK3曲面がしばしば表れることがある。実際に、本研究においてもK3曲面の結果をこのような文脈において応用して成果を得ることができた。このような意味において、本研究の成果が今後応用されることが期待される。
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