| Project/Area Number |
22540052
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| Research Category |
Grant-in-Aid for Scientific Research (C)
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| Allocation Type | Single-year Grants |
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| Section | 一般 |
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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, 大学院・理工学研究科, 教授 (30211395)
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| Co-Investigator(Renkei-kenkyūsha) |
OKA Mutsuo 東京理科大学, 理学部, 教授 (40011697)
SHIMADA Ichiro 広島大学, 大学院・理学研究科, 教授 (10235616)
NAKAMURA Hiroaki 岡山大学, 自然科学研究科, 教授 (60217883)
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| Project Period (FY) |
2010 – 2012
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| Project Status |
Completed (Fiscal Year 2012)
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| Budget Amount *help |
¥4,160,000 (Direct Cost: ¥3,200,000、Indirect Cost: ¥960,000)
Fiscal Year 2012: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
Fiscal Year 2011: ¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000)
Fiscal Year 2010: ¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000)
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| Keywords | 分解曲線 / 楕円曲面 / Galois被覆 / 楕円曲面の切断 / アーベル・ヤコビ写像 / Alexander多項式 / 二面体被覆 / section / Zariski pair / conic-line arrangement / splitting curve / Mordell-Weil群 |
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| Research Abstract |
We studied Galois covers, in particular, double covers of algebraic surfaces from a view point of number theory, and applied our result to study topology of open algebraic surfaces. We studied splitting curves in double covers, number theory of elliptic curves over the rational function field of one variable and their application to explicit construction problem for Galois covers. Based on our results, we gave examples of Zariski pairs for conic-line arrangements and Zariski N-plets for conic arrangements.
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