Arithmetic aspects of Mordell-Weil lattices of elliptic K3 surfaces
| Project/Area Number |
26400023
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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 | Chuo University |
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Principal Investigator |
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| Project Period (FY) |
2014-04-01 – 2018-03-31
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| Project Status |
Completed (Fiscal Year 2017)
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| Budget Amount *help |
¥3,640,000 (Direct Cost: ¥2,800,000、Indirect Cost: ¥840,000)
Fiscal Year 2017: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2016: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2015: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2014: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
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| Keywords | K3曲面 / 楕円曲面 / Mordell－Weil格子 / 塩田－猪瀬構造 / Jacobi多様体 / 数論幾何 / Mordell-Weil格子 / 数論幾何学 / 国際研究者交流 アメリカ合衆国 |
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| Outline of Final Research Achievements |
Using certaine elliptic fibrations on a K3 surfaces with so-called Shioda-Inose structure, we constructed elliptic K3 surfaces with high Mordell-Weil rank, and studied their generators. In particular, we found generators of a Mordell-Weil lattice of rank 18 of an elliptic K3 surface obtained from a Kummer surface of product type. Also, starting from a Kummer surface of the Jacobian of a curve of genus 2, we constructed an elliptic K3 surface of Mordell-Weil rank 15, which could not be obtained from the Kummer surfaces of product type. To study the field of definition of such Mordell-Weil lattice, we studied the moduli space of principally polarized abelian surfaces with full level structure of level 3.
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Report
(5 results)
Research Products
(14 results)
