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Deeper Understanding of Relations between Mirror Syemmetry and Geometry of Moduli Spaces

Research Project

Project/Area Number 17K05214
Research Category

Grant-in-Aid for Scientific Research (C)

Allocation TypeMulti-year Fund
Section一般
Research Field Geometry
Research InstitutionOkayama University (2020-2021)
Hokkaido University (2017-2019)

Principal Investigator

Jinzenji Masao  岡山大学, 自然科学学域, 教授 (20322795)

Project Period (FY) 2017-04-01 – 2022-03-31
Project Status Completed (Fiscal Year 2021)
Budget Amount *help
¥3,640,000 (Direct Cost: ¥2,800,000、Indirect Cost: ¥840,000)
Fiscal Year 2021: ¥650,000 (Direct Cost: ¥500,000、Indirect Cost: ¥150,000)
Fiscal Year 2020: ¥650,000 (Direct Cost: ¥500,000、Indirect Cost: ¥150,000)
Fiscal Year 2019: ¥650,000 (Direct Cost: ¥500,000、Indirect Cost: ¥150,000)
Fiscal Year 2018: ¥650,000 (Direct Cost: ¥500,000、Indirect Cost: ¥150,000)
Fiscal Year 2017: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Keywordsミラー対称性 / モジュライ空間 / 擬写像 / トーリック幾何学 / 複素幾何学 / 交点数 / 過剰交叉 / コンパクト化 / 擬写像のモジュライ空間 / 位相的ヤン‐ミルズ理論 / 複素グラスマン多様体 / 自由フェルミオン表現 / コホモロジー環 / 周期積分 / 種数1のグロモフ‐ウィッテン不変量 / 留数積分表示 / 複素幾何 / 複素構造の変形 / 経路積分 / ボットの留数定理 / オイラーの五角数定理 / ミラー / 位相的シグマ模型 / トーリック多様体 / チャウ環 / グロモフ-ウィッテン不変量 / 有理写像
Outline of Final Research Achievements

Most important achivement in this research project is the geometrical proof of the mirror theorem of genus 0 Gromov-Witten invariants of projettive hypersurfaces, which was done by applying all the previous results on intersectiopn numbers of moduli space of quasimaps constructed by myself. The paper that presents the proof
is still under reviewing process, and I have to care about how the proof is evaluated by mathematical community. On the other hand, I collaborated with graduate students in may laboratory and pubrished several papers not only on mirror symmetry but also on new topics that connect mathematical physics with geometry.

Academic Significance and Societal Importance of the Research Achievements

本研究課題期間中において、私は2冊の著書を出版した。一つは、古典的ミラー対称性の紹介とそれに関する私の研究結果を併記した英語の本で、本研究課題の成果を広く社会に紹介する上で大きな役割を果たしたと言える。もう一つは、物理学生のために複素幾何学を紹介する専門書で、これは私がミラー対称性の研究をする上で使ってきた知識を後進の人達に伝える目的で書かれたものである。今後、このような本が必要とされる機会は増えると思われ、その意味でも大いに学術的意義、社会的意義があるとアピールしたいところである。

Report

(6 results)
  • 2021 Annual Research Report   Final Research Report ( PDF )
  • 2020 Research-status Report
  • 2019 Research-status Report
  • 2018 Research-status Report
  • 2017 Research-status Report
  • Research Products

    (8 results)

All 2021 2020 2019 2018

All Journal Article (3 results) (of which Peer Reviewed: 2 results) Presentation (2 results) (of which Int'l Joint Research: 1 results,  Invited: 2 results) Book (3 results)

  • [Journal Article] Moduli space of quasimaps from ℙ<sup>1</sup> with two marked points to ℙ(1, 1, 1, 3) and 𝑗-invariant2021

    • Author(s)
      Masao Jinzenji, Hayato Saito
    • Journal Title

      Journal of the Mathematical Society of Japan

      Volume: 73 Issue: 4 Pages: 995-1018

    • DOI

      10.2969/jmsj/83148314

    • NAID

      130008106930

    • ISSN
      0025-5645, 1881-1167, 1881-2333
    • Related Report
      2021 Annual Research Report 2020 Research-status Report
    • Peer Reviewed
  • [Journal Article] Holomorphic Vector Field and Topological Sigma Model on CP^1 World Sheet2020

    • Author(s)
      Masao Jinzenji, Ken Kuwata
    • Journal Title

      International Journal of Modern Physics A

      Volume: 35 Issue: 30 Pages: 2050192-2050192

    • DOI

      10.1142/s0217751x20501924

    • Related Report
      2020 Research-status Report
    • Peer Reviewed
  • [Journal Article] 素粒子物理とカラビ・ヤウ多様体 : 一物理学院生が代数幾何学に巻き込まれた経緯2018

    • Author(s)
      秦泉寺 雅夫
    • Journal Title

      数理科学

      Volume: 56巻10月号

    • Related Report
      2018 Research-status Report
  • [Presentation] Geometrical Proof of Generalized Mirror Transformation of Projective Hypersurfaces2020

    • Author(s)
      Masao Jinzenji
    • Organizer
      Rikkyo MathPhys 2020
    • Related Report
      2019 Research-status Report
    • Int'l Joint Research / Invited
  • [Presentation] Geometrical Proof of Generalized Mirror Transformation of Projective Hypersurfaces2018

    • Author(s)
      Masao Jinzenji
    • Organizer
      Seminar in National Center of Theoretical Sciences Physics Division
    • Related Report
      2017 Research-status Report
    • Invited
  • [Book] 数物系のためのミラー対称性入門【電子版】2021

    • Author(s)
      秦泉寺雅夫
    • Total Pages
      214
    • Publisher
      サイエンス社
    • ISBN
      9784781999838
    • Related Report
      2020 Research-status Report
  • [Book] 物理系のための複素幾何入門2019

    • Author(s)
      秦泉寺雅夫
    • Total Pages
      232
    • Publisher
      サイエンス社
    • ISBN
      4910054700794
    • Related Report
      2019 Research-status Report
  • [Book] Classical Mirror Symmetry2018

    • Author(s)
      Masao Jinzenji
    • Total Pages
      140
    • Publisher
      Springer
    • ISBN
      9789811300561
    • Related Report
      2017 Research-status Report

URL: 

Published: 2017-04-28   Modified: 2023-01-30  

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