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Study on Mirror Symmetry and Geometry of Moduli Space

Research Project

Project/Area Number 25400061
Research Category

Grant-in-Aid for Scientific Research (C)

Allocation TypeMulti-year Fund
Section一般
Research Field Geometry
Research InstitutionHokkaido University

Principal Investigator

Jinzenji Masao  北海道大学, 理学(系)研究科(研究院), 准教授 (20322795)

Project Period (FY) 2013-04-01 – 2016-03-31
Project Status Completed (Fiscal Year 2015)
Budget Amount *help
¥2,600,000 (Direct Cost: ¥2,000,000、Indirect Cost: ¥600,000)
Fiscal Year 2015: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000)
Fiscal Year 2014: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000)
Fiscal Year 2013: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Keywordsミラー定理 / グロモフ-ウィッテン不変量 / 留数積分表示 / 対角的寄与 / 射影空間内の超曲面 / 射影空間の超曲面 / 留数積分 / ミラー対称性 / 対角アノマリー / グロモフ--ウィッテン不変量 / モジュライ空間 / コンパクト化 / ミラー写像 / 擬写像
Outline of Final Research Achievements

I invented a recipe to cancel all the diagonal contributions, which are obstacles to represent genus 0 Gromov-Witten invariants of projective hypersurfaces in terms of residue integrals. Using this recipe, I completed residue integral representation of the Gromov-Witten invariants. This result enables me to give a direct and geometrical proof of the mirror theorem of projective hypersurfaces. But it seems to take a little more time to complete
the full paper on this result.

Report

(4 results)
  • 2015 Annual Research Report   Final Research Report ( PDF )
  • 2014 Research-status Report
  • 2013 Research-status Report
  • Research Products

    (14 results)

All 2016 2015 2014 2013 Other

All Journal Article (4 results) (of which Peer Reviewed: 3 results,  Open Access: 1 results) Presentation (9 results) (of which Invited: 8 results) Book (1 results)

  • [Journal Article] Multi-point virtual structure constants and mirror computation of CP^2-model.2014

    • Author(s)
      Masao Jinzenji
    • Journal Title

      Lie Theory and Its Applications in Physics, Springer Proceedings in Mathematics & Statistics

      Volume: 111 Pages: 415424-415424

    • Related Report
      2014 Research-status Report
    • Peer Reviewed
  • [Journal Article] 多点仮想構造定数とCP^2の種数0のグロモフ-ウィッテン不変量のミラー対称性的計算法について2014

    • Author(s)
      秦泉寺雅夫
    • Journal Title

      数理解析研究所講究録

      Volume: 1918 Pages: 8897-8897

    • Related Report
      2014 Research-status Report
    • Open Access
  • [Journal Article] Open Virtual Structure Constants and Mirror Computation of Open Gromov-Witten Invariants of Projective Hypersurfaces2014

    • Author(s)
      Masao Jinzenji, Masahode Shimizu.
    • Journal Title

      International Journal of Geometric Methods in Modern Physics

      Volume: Vol. 11, No. 1 Issue: 01 Pages: 1450005-1450005

    • DOI

      10.1142/s0219887814500054

    • Related Report
      2013 Research-status Report
    • Peer Reviewed
  • [Journal Article] Mirror Map as Generating Function of Intersection Numbers: Toric Manifolds with Two Kähler Forms2013

    • Author(s)
      Masao Jinzenji.
    • Journal Title

      Communications in Mathematical Physics

      Volume: 323 Issue: 2 Pages: 747-811

    • DOI

      10.1007/s00220-013-1786-y

    • Related Report
      2013 Research-status Report
    • Peer Reviewed
  • [Presentation] Direct proof of mirror theorem of projective hypersurfaces2016

    • Author(s)
      秦泉寺雅夫
    • Organizer
      立教大学数理物理学研究センター臨時セミナー
    • Place of Presentation
      立教大学(東京都・豊島区)
    • Year and Date
      2016-02-24
    • Related Report
      2015 Annual Research Report
    • Invited
  • [Presentation] Toward direct proof of mirror theorem of projective hypersurfaces2015

    • Author(s)
      秦泉寺雅夫
    • Organizer
      日本数学会秋季総合分科会
    • Place of Presentation
      京都産業大学(京都府・京都市)
    • Year and Date
      2015-09-15
    • Related Report
      2015 Annual Research Report
  • [Presentation] Toward Direct Proof of Mirror Theorem of Projective Hypersurfaces.2014

    • Author(s)
      Masao Jinzenji
    • Organizer
      Mathematics Inspired by String Theory.
    • Place of Presentation
      Tsinghua Sanya International Mathematics Forum (中国)
    • Year and Date
      2014-12-10
    • Related Report
      2014 Research-status Report
    • Invited
  • [Presentation] Multi-Point Virtual Structure Constants and Mirror Computation of CP^2 - model

    • Author(s)
      Masao Jinzenji
    • Organizer
      X. International Workshop LIE THEORY AND ITS APPLICATIONS IN PHYSICS
    • Place of Presentation
      Institute for Nuclear Research and Nuclear Energy(ブルガリア)
    • Related Report
      2013 Research-status Report
    • Invited
  • [Presentation] Mirror Map as Generating Function of Intersection Numbers

    • Author(s)
      Masao Jinzenji
    • Organizer
      The 6th Pacific RIM Conference on Mathematics 2013
    • Place of Presentation
      札幌コンベンションセンター(北海道)
    • Related Report
      2013 Research-status Report
    • Invited
  • [Presentation] Mirror Map as Generating Function of Intersection Numbers

    • Author(s)
      Masao Jinzenji
    • Organizer
      Geometry and Topology Workshop
    • Place of Presentation
      香港中文大学(中国)
    • Related Report
      2013 Research-status Report
    • Invited
  • [Presentation] Mirror Map as Generating Function of Intersection Numbers

    • Author(s)
      秦泉寺雅夫
    • Organizer
      立教大学数理物理学研究センター 臨時セミナー
    • Place of Presentation
      立教大学(東京都)
    • Related Report
      2013 Research-status Report
    • Invited
  • [Presentation] Mirror Map as Generating Function of Intersection Numbers

    • Author(s)
      秦泉寺雅夫
    • Organizer
      研究集会「頂点作用素代数と超弦理論」
    • Place of Presentation
      立教大学(東京都)
    • Related Report
      2013 Research-status Report
    • Invited
  • [Presentation] Multi-Point Virtual Structure Constants and Mirror Computation of CP^2-model

    • Author(s)
      秦泉寺雅夫
    • Organizer
      研究集会「ミラー対称性の展望」
    • Place of Presentation
      京都大学(京都市)
    • Related Report
      2013 Research-status Report
    • Invited
  • [Book] 数物系のためのミラー対称性入門2014

    • Author(s)
      秦泉寺 雅夫
    • Total Pages
      216
    • Publisher
      サイエンス社
    • Related Report
      2014 Research-status Report

URL: 

Published: 2014-07-25   Modified: 2019-07-29  

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