| Project/Area Number |
15340049
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| Research Category |
Grant-in-Aid for Scientific Research (B)
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| Allocation Type | Single-year Grants |
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| Section | 一般 |
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| Research Field |
Basic analysis
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| Research Institution | Osaka City University |
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Principal Investigator |
IMAYOSHI Yoichi Osaka City University, Graduate School of Science, Professor, 大学院・理学研究科, 教授 (30091656)
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| Co-Investigator(Kenkyū-buntansha) |
KAWAUCHI Akio Osaka City University, Graduate School of Science, Professor, 大学院・理学研究科, 教授 (00112524)
KOMORI Youhei Osaka City University, Graduate School of Science, Associate Professor, 大学院・理学研究科, 助教授 (70264794)
NOGUCHI Junjiro The University of Tokyo, Graduate School of Mathematical Sciences, Professor, 大学院・数理科学研究科, 教授 (20033920)
MATSUMOTO Yukio The University of Tokyo, Graduate School of Mathematical Sciences, Professor, 大学院・数理科学研究科, 教授 (20011637)
SHIGA Hiroshige Tokyo Institute of Technology, Graduate School of Science and Engineering, Professor, 大学院・理工学研究科, 教授 (10154189)
佐官 謙一 大阪市立大学, 大学院・理学研究科, 助教授 (70110856)
足利 正 東北学院大学, 工学部, 教授 (90125203)
加藤 信 大阪市立大学, 大学院・理学研究科, 助教授 (10243354)
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| Project Period (FY) |
2003 – 2005
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| Project Status |
Completed (Fiscal Year 2005)
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| Budget Amount *help |
¥8,100,000 (Direct Cost: ¥8,100,000)
Fiscal Year 2005: ¥2,600,000 (Direct Cost: ¥2,600,000)
Fiscal Year 2004: ¥2,400,000 (Direct Cost: ¥2,400,000)
Fiscal Year 2003: ¥3,100,000 (Direct Cost: ¥3,100,000)
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| Keywords | Riemann surface / holomorphic family / monodromy / mapping class group / Teichmuller space / function field / Diophantine problem / 普遍被覆面 / 普遍被覆空間 |
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| Research Abstract |
Applying Teichmuller space, we studied Diophantine problem over function fields and holomorphic familes of Riemann surfaces, and we obtained the following results :
(1)We determined all the holomorphic sections of holomorphic families of closed Riemann surfaces of genus 2 induced by certain Kodaira surfaces. Using elliptic functions, we got defining equations of these families, and so obtained all the solutions of the Diophantine problem for these defining equations.
(2)For a hyperbolic Riemann surface S of type (g,n), let B={(x,y)∈S×S|x≠y}, M={(x,y,z)∈S×S×S|x≠y,y≠z,z≠x}, and π:M→B the canonical projection. We determined completely types of Bers for elements of monodromy of the holomorphic family (M,π,B).
(3)For a holomorphic family (M,π,R) over a Riemann surface R, we studied complex analytic properties of the universal covering space of M.
(4)For a given pseudo-periodic map f of negative type, we constructed a holomorphic family (M,π,Δ^*) over the punctured unit disc Δ^* with monodromy f. This is an alternative proof for a theorem due to Matsumoto and Montesinos, and gives a systematic method to construct these holomorphic families.
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