2017 Fiscal Year Final Research Report
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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| Keywords | K3曲面 / 楕円曲面 / Mordell－Weil格子 / 塩田－猪瀬構造 / Jacobi多様体 |
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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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| Free Research Field |
数論幾何
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