• Search Research Projects
  • Search Researchers
  • How to Use
  1. Back to previous page

Special functions and algebraic geometry

Research Project

Project/Area Number 18K03236
Research Category

Grant-in-Aid for Scientific Research (C)

Allocation TypeMulti-year Fund
Section一般
Review Section Basic Section 11010:Algebra-related
Research InstitutionUniversity 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)
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 $F_C$

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。

Report

(4 results)
  • 2020 Annual Research Report   Final Research Report ( PDF )
  • 2019 Research-status Report
  • 2018 Research-status Report
  • Research Products

    (1 results)

All 2020

All Journal Article (1 results) (of which Peer Reviewed: 1 results)

  • [Journal Article] Picard-Vessiot groups of Lauricella's hypergeometric systems EC and Calabi-Yau varieties arising integral representations2020

    • Author(s)
      Goto Yoshiaki、Koike Kenji
    • Journal Title

      Journal of the London Mathematical Society

      Volume: - Issue: 1 Pages: 22-42

    • DOI

      10.1112/jlms.12311

    • Related Report
      2020 Annual Research Report
    • Peer Reviewed

URL: 

Published: 2018-04-23   Modified: 2022-01-27  

Information User Guide FAQ News Terms of Use Attribution of KAKENHI

Powered by NII kakenhi