Arithmetic and the Abel Jacobi map on elliptic surfaces and their applications
| Project/Area Number |
25610007
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| Research Category |
Grant-in-Aid for Challenging Exploratory Research
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| Allocation Type | Multi-year Fund |
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| Research Field |
Algebra
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| Research Institution | Tokyo Metropolitan University |
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Principal Investigator |
TOKUNAGA HIROO 首都大学東京, 理工学研究科, 教授 (30211395)
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| Co-Investigator(Kenkyū-buntansha) |
内山 成憲 首都大学東京, 理工学研究科, 教授 (40433172)
内田 幸寛 首都大学東京, 理工学研究科, 准教授 (90533258)
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| Research Collaborator |
BANNAI SHINZO 茨城工業高等専門学校, 講師 (20732556)
SHIRANE TAKETO 宇部工業高等専門学校, 准教授 (70615161)
Guerville-Balle Benoit 東京学芸大学
Tumenbayar Kuhlan National University of Mongolia
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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 |
¥3,900,000 (Direct Cost: ¥3,000,000、Indirect Cost: ¥900,000)
Fiscal Year 2015: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2014: ¥1,560,000 (Direct Cost: ¥1,200,000、Indirect Cost: ¥360,000)
Fiscal Year 2013: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
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| Keywords | 楕円曲面 / Mordell Weil群 / 整切断 / 2重切断 / Zariski ペア / contact conic / k Artal arrangement / bisection / 有理楕円曲面 / Zariski N 組 / Zariski 対 / 楕円曲線 / 不定方程式 / 暗号 / ペアリング / Zariski N組 / Jacobi多様体 / ガロア分岐被覆 / Zariski k組 / Mordell-Weil群 / Mordell-Weil格子 |
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| Outline of Final Research Achievements |
We study arithmetic of rational points and Abel-Jacobi map for an elliptic curve appeared as the generic fiber of an elliptic surface S over a projective line. More precisely, we study curves on S given by the sum of two rational points or the duplication of a rational point. We also study bisections on S and curves determined by the bisections.
As applications, we study quasi torus decompositions of plane curves and Zariski N plet. Precisely, we give examples of Zariski pairs for conic-line arrangements, Zariski N-plets for conic arrangements, and weak contact conics for plane quartic curves.
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Report
(5 results)
Research Products
(32 results)
