| Project/Area Number |
25400052
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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 | Rikkyo University |
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Principal Investigator |
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| Co-Investigator(Renkei-kenkyūsha) |
AOKI Noboru 立教大学, 理学部, 教授 (30183130)
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| Project Period (FY) |
2013-04-01 – 2017-03-31
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| Project Status |
Completed (Fiscal Year 2016)
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| Budget Amount *help |
¥3,120,000 (Direct Cost: ¥2,400,000、Indirect Cost: ¥720,000)
Fiscal Year 2015: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2014: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2013: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
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| Keywords | 代数幾何学 / モーデル・ヴェイユ格子 / ガロア表現 / 有理楕円曲面 / フェルマー曲面 / ネロン・セヴェリ格子 / 高種数ファイブレーション / 乗法的卓越族 / K３曲面 / 楕円曲面 / 高種数曲線ファイブレーション / ネロン・セヴェリ群 / ピカール数 / 3次曲面と２７直線 / 楕円ファイブレーション / ハイト公式 / ３次曲面と２７直線 / ワイヤストラス変換 |
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| Outline of Final Research Achievements |
The study of Mordell-Weil lattices has been focused on the following subjects.
1. The multiplicative excellent family of rational elliptic surfaces has the defining Weierstrass equation such that the coefficients form a set of fundamental invariants of the Weyl group in a Laurent polynomial ring. So the Mordell-Weil lattices, originally of Diophantine nature, can have a direct connection with the fundamental representations of Lie groups of the corresponding type, which admits various applications.
2. We have examined the structure of Mordell-Weil lattices of higher genus fibration on a Fermat surface. If the degree is relatively prime to 6, the structure (rank, height pairing etc.) is determined. More generally, the method applies to smooth surfaces containing a line.
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