Geometrical Study of Mirror Symmetry

• Project/Area Number: 22540061
• Research Category: Grant-in-Aid for Scientific Research (C)
• Allocation Type: Single-year Grants
• Section: 一般
• Research Field: Geometry
• Research Institution: Hokkaido University
• Principal Investigator: JINZENJI Masao 北海道大学, 大学院・理学研究院, 准教授 (20322795)
• Project Period (FY): 2010 – 2012
• Project Status: Completed (Fiscal Year 2012)
• Budget Amount: ¥2,470,000 (Direct Cost: ¥1,900,000、Indirect Cost: ¥570,000); Fiscal Year 2012: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000); Fiscal Year 2011: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000); Fiscal Year 2010: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
• Keywords: ミラー写像 / ミラー対称性 / モジュライ空間 / 交点数 / 固定点定理 / 擬写像 / グロモフ‐ウィッテン不変量 / コンパクト化 / 仮想構造定数 / 開弦 / 多項式写像

Research Abstract

We reconstructed the mirror map, which is used in the mirror computation of Gromov-Witten invariants, as a generating function of intersection numbers of the moduli space of quasi maps. With this result, we reinterpreted the mirror computation of Gromov-Witten invariants as a way of computing Gromov-Witten invariants by using the difference of compactification of the moduli space of holomorphic maps. We also used this reconstruction to generalize the mirror computation of open Gromov-Witten invariants to wide class of complex manifolds.

Research Products

• [Journal Article] Mirror Map as Generating Function of Intersection Numbers. (2013)
  • Author(s): Masao Jinzenji.
  • Journal Title: Lie Theory and its Applications in Physics IX. International Workshop Series: Springer Proceedings in Mathematics & Statistics Volume: Vol. 36. Pages: 181-189
  • Peer Reviewed
• [Journal Article] Mirror Map as Generating Function of Intersection Numbers (2013)
  • Author(s): Masao Jinzenji
  • Journal Title: Lie Theory and Its Applications in Physics：Springer Proceedings in Mathematics & Statisticｓ Volume: Vol. 36 Pages: 181-190
  • Peer Reviewed
• [Journal Article] Direct Proof of Mirror Theorem ofProjective Hypersurfaces up to degree 3Rational Curves. (2011)
  • Author(s): Masao Jinzenji .
  • Journal Title: Journal of Geometry and Physics Volume: Vol. 61, Issue 8 Pages: 1564-1573
  • Peer Reviewed
• [Journal Article] Open Virtual Structure Constants and Mirror Computation of Open Gromov-Witten Invariants of Projective Hypersurfaces.
  • Author(s): Masao Jinzenji
  • Journal Title: Masahide Shimizu. International Journal of Geometric Methods in Modern Physics Volume: (掲載予定)
  • Peer Reviewed
• [Journal Article] Mirror Map as Generating Function of Intersection Numbers: Toric Manifolds with Two Kahler Forms.
  • Author(s): Masao Jinzenji .
  • Journal Title: Communications in Mathematical Physics Volume: (掲載予定)
  • Peer Reviewed
• [Journal Article] Direct Proof of Mirror Theorem of Projective Hypersurfaces up to degree 3 Rational Curves
  • Author(s): Masao Jinzenji
  • Journal Title: Journal of Geometry and Physics Volume: (掲載予定)
  • Peer Reviewed
• [Presentation] Multi-Point Virtual Structure Constants and Mirror Computation of CP^2-model (2013)
  • Author(s): 秦泉寺雅夫
  • Organizer: 日本数学会2013年年会
  • Place of Presentation: 於京都大学京都市
  • Year and Date: 2013-03-22
• [Presentation] Multi-point virtual structure constants and mirror computation of CP^2-model (2013)
  • Author(s): Masao Jinzenji
  • Organizer: ２０１３年日本数学会年会
  • Place of Presentation: 京都大学 （京都市）
• [Presentation] Mirror Map as Generating Function of Intersection Numbers (2012)
  • Author(s): Masao Jinzenji
  • Organizer: 北大‐ソウル大ジョイントシンポジウム 幾何とトポロジーの関連分野における最近の進展
  • Place of Presentation: 北海道大学 （札幌市）
  • Invited
• [Presentation] Open Virtual Structure Constants and Mirror Computation of Open Gromov-Witten Invariants of Projective Hypersurfaces (2011)
  • Author(s): Masao Jinzenji .
  • Organizer: Seminar on Symplectic Geometry and Mathematical Physics. Beijing International Center for MathematicalResearch.
  • Place of Presentation: 北京、中国
  • Year and Date: 2011-12-01
• [Presentation] Open Virtual Structure Constants and Mirror Computation of Open Gromov-Witten Invariants of Projective Hypersurfaces (2011)
  • Author(s): 秦泉寺雅夫
  • Organizer: 首 都大学東京幾何学セミナー.
  • Place of Presentation: 八王子市
  • Year and Date: 2011-11-11
• [Presentation] Mirror Map as Generating Function of Intersection Numbers (2011)
  • Author(s): Masao Jinzenji .
  • Organizer: International Workshop: LIE THEORY AND ITS APPLICATIONS IN PHYSICS. Bulgarian Academy of Sciences,Institute for Nuclear Research and NuclearEnergy.
  • Place of Presentation: バルナ、ブルガリア
  • Year and Date: 2011-06-21
• [Presentation] Mirror Map as Generating Function of Intersection Numbers (2011)
  • Author(s): Masao Jinzenji
  • Organizer: IX International Workshop : Lie Theory and Its Applications In Physics
  • Place of Presentation: Institute for Nuclear Research and Nuclear Energy (Bulgaria)(招待講演)
  • Year and Date: 2011-06-21
• [Presentation] MirrorMapasGeneratingFunctionofIntersectionNumbers (2010)
  • Author(s): 秦泉寺雅夫
  • Organizer: 日本数学会2010年秋季総合分科会(於名古屋大学).(一般公演).
  • Place of Presentation: 於京都大学名古屋市
  • Year and Date: 2010-09-22
• [Presentation] Mirror map as generating function of intersection numbers (2010)
  • Author(s): 秦泉寺雅夫
  • Organizer: 日本数学会秋季総合分科会
  • Place of Presentation: 名古屋大学
  • Year and Date: 2010-09-22