Special functions and algebraic geometry
Project/Area Number |
18K03236
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Research Category |
Grant-in-Aid for Scientific Research (C)
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Allocation Type | Multi-year Fund |
Section | 一般 |
Review Section |
Basic Section 11010:Algebra-related
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Research Institution | University of Yamanashi |
Principal Investigator |
KOIKE Kenji 山梨大学, 大学院総合研究部, 准教授 (20362056)
|
Project Period (FY) |
2018-04-01 – 2021-03-31
|
Project Status |
Completed (Fiscal Year 2020)
|
Budget Amount *help |
¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
Fiscal Year 2020: ¥390,000 (Direct Cost: ¥300,000、Indirect Cost: ¥90,000)
Fiscal Year 2019: ¥390,000 (Direct Cost: ¥300,000、Indirect Cost: ¥90,000)
Fiscal Year 2018: ¥520,000 (Direct Cost: ¥400,000、Indirect Cost: ¥120,000)
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Keywords | 超幾何関数 / 代数多様体 / モノドロミー / 特殊関数 / 代数幾何 |
Outline of Final Research Achievements |
We studied the Zariski closure of the monodromy group for Lauricella's hypergeometric function F_C applying results of F. Beukers and G. Heckman. If the monodoromy group acts irreducibly on the solution space, the Zariski closure is one of classical groups GL_n, O_n and Sp_n. We also considered K3 surfaces and Calabi-Yau varieties arising from integral representations of $F_C$
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Academic Significance and Societal Importance of the Research Achievements |
多変数超幾何関数のモノドロミー群に関しては多くの研究があるが,そのZariski閉包やArithmeticyについては十分な研究はなされていない。本研究でLauricellaの超幾何関数F_Cに対して行われたモノドロミー群のZariski閉包の分類は,多変数超幾何関数の変数の個数に制限を与えずに得られた最初の結果であると言える。この結果は,F_Cのモノドロミー群のarithmeticyに関する研究への第1歩となだろう。
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Report
(4 results)
Research Products
(1 results)