Study on Mirror Symmetry and Geometry of Moduli Space

• Project/Area Number: 25400061
• Research Category: Grant-in-Aid for Scientific Research (C)
• Allocation Type: Multi-year Fund
• Section: 一般
• Research Field: Geometry
• Research Institution: Hokkaido 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: ¥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.

Research Products

• [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
  • 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
  • Open Access
• [Journal Article] Open Virtual Structure Constants and Mirror Computation of Open Gromov-Witten Invariants of Projective Hypersurfaces (2014)
  • 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
  • Peer Reviewed
• [Journal Article] Mirror Map as Generating Function of Intersection Numbers: Toric Manifolds with Two Kähler Forms (2013)
  • Author(s): Masao Jinzenji.
  • Journal Title: Communications in Mathematical Physics Volume: 323 Issue: 2 Pages: 747-811
  • DOI: 10.1007/s00220-013-1786-y
  • Peer Reviewed
• [Presentation] Direct proof of mirror theorem of projective hypersurfaces (2016)
  • 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
  • Invited
• [Presentation] Toward direct proof of mirror theorem of projective hypersurfaces (2015)
  • 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
• [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
  • 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）
  • 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)
  • 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)
  • 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）
  • 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）
  • 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）
  • 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