| Project/Area Number |
25400033
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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 | Hokkaido University |
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Principal Investigator |
Matsumoto Keiji 北海道大学, 理学(系)研究科(研究院), 教授 (30229546)
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| Co-Investigator(Renkei-kenkyūsha) |
OHARA Katsuyoshi 金沢大学, 数物科学系, 准教授 (00313635)
TERASOMA Tomohide 東京大学, 数理科学研究科, 教授 (50192654)
YOSHIDA Masaaki 九州大学, 名誉教授 (30030787)
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| Project Period (FY) |
2013-04-01 – 2016-03-31
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| Project Status |
Completed (Fiscal Year 2015)
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| Budget Amount *help |
¥4,940,000 (Direct Cost: ¥3,800,000、Indirect Cost: ¥1,140,000)
Fiscal Year 2015: ¥1,820,000 (Direct Cost: ¥1,400,000、Indirect Cost: ¥420,000)
Fiscal Year 2014: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
Fiscal Year 2013: ¥1,820,000 (Direct Cost: ¥1,400,000、Indirect Cost: ¥420,000)
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| Keywords | 超幾何関数 / 超幾何微分方程式 / 局所系係数ホモロジー群 / 局所系係数コホモロジー群 / 交点形式 / モノドロミー表現 / 接続行列 / 超幾何微分方程式系 / twisted homology group / twisted cohomology group / twsited homology group / 周期積分 / テータ関数 |
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| Outline of Final Research Achievements |
Period integrals of algebraic varieties can be regarded as hypergeometric functions, and they satisfy a system of linear differential equations so that
a vector space of its local solutions (a local solution space) is finite dimensional. For some of such systems, I characterize the monodromy representation which describe a global property of a map defined by a basis of its local solution space, and the connection matrix of the first order differential equation with a vector-valued unknown function equivalent to the original system. In this study, I make clear their structures by using the intersection forms defined between twisted (co)homology groups which are induced from period integrals.
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