Geometry of orthogonal modular varieties
| Project/Area Number |
17K14158
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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 | Tokyo Institute of Technology |
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Principal Investigator |
Ma Shouhei 東京工業大学, 理学院, 准教授 (80633255)
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| Project Period (FY) |
2017-04-01 – 2021-03-31
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| Project Status |
Completed (Fiscal Year 2020)
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| Budget Amount *help |
¥2,600,000 (Direct Cost: ¥2,000,000、Indirect Cost: ¥600,000)
Fiscal Year 2020: ¥650,000 (Direct Cost: ¥500,000、Indirect Cost: ¥150,000)
Fiscal Year 2019: ¥650,000 (Direct Cost: ¥500,000、Indirect Cost: ¥150,000)
Fiscal Year 2018: ¥650,000 (Direct Cost: ¥500,000、Indirect Cost: ¥150,000)
Fiscal Year 2017: ¥650,000 (Direct Cost: ¥500,000、Indirect Cost: ¥150,000)
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| Keywords | 直交型モジュラー多様体 / モジュラー多様体 / K3曲面 / モジュライ空間 / ボーチャーズ積 / モジュラー形式 |
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| Outline of Final Research Achievements |
I studied the birational type of orthogonal modular varieties and the moduli spaces of pointed K3 surfaces. In particular, I proved that most orthogonal modular varieties are of general type in dimension greater than 20. As a byproduct I proved a conjecture of Gritsenko and Nikulin on reflective modular forms. For the moduli spaces of pointed K3 surfaces, I studied the transition point of Kodaira dimension. I also studied some topics related to Borcherds products, such as equivariant Gauss sum, quasi-pullback formula and a new product structure.
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| Academic Significance and Societal Importance of the Research Achievements |
直交型モジュラー多様体は代数幾何、数論、表現論が交わる豊かな研究対象である。本研究では直交型モジュラー多様体のいくつかの幾何学的性質を研究した。特に高次元でほとんど一般型になるという結果は、「大自然はやはり複雑で奥深い」ということをある意味定量的に示したものと言える。
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Report
(5 results)
Research Products
(16 results)
