Period integrals, derived categories, and geometries of Moduli spaces

• Project/Area Number: 18540014
• Research Category: Grant-in-Aid for Scientific Research (C)
• Allocation Type: Single-year Grants
• Section: 一般
• Research Field: Algebra
• Research Institution: The University of Tokyo
• Principal Investigator: HOSONO Shinobu The University of Tokyo, 大学院・数理科学研究科, 准教授 (60212198)
• Project Period (FY): 2006 – 2009
• Project Status: Completed (Fiscal Year 2009)
• Budget Amount: ¥4,280,000 (Direct Cost: ¥3,500,000、Indirect Cost: ¥780,000); Fiscal Year 2009: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000); Fiscal Year 2008: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000); Fiscal Year 2007: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000); Fiscal Year 2006: ¥900,000 (Direct Cost: ¥900,000)
• Keywords: カラビ・ヤウ多様体 / ミラー対称性 / グロモフ・ウイッテン不変量 / 超幾何微分方程式 / トーリック多様体 / 弦理論 / グロモフ・ウィッテン不変量 / 周期積分 / モジュラー形式 / ミラー多様体 / ストークス行列

Research Abstract

Manifolds are mathematical objects which generalize curves in a plane, surfaces in a space, etc. In modern physics, manifolds are used as a mathematical model of the universe. Over the last two decades, Calabi-Yau manifolds have been attracting attentions of both physicists and mathematicians. In this research, a detailed mathematical study has been done on some geometric invariants, called Gromov-Witten invariants, of Calabi-Yau manifolds. In particular mathematical structures in a certain recursive equation for computing the invariants have been revealed.

Research Products

• [Journal Article] BCOV rings and holomorphic anomaly equation (2010)
  • Author(s): S. Hosono
  • Journal Title: Adv.Studies in Pure Math. Vol. 59(印刷中)
  • Peer Reviewed
• [Journal Article] BCOV ring and holomorphic anomaly equation (2010)
  • Author(s): Hosono, Shinobu
  • Journal Title: Advanced Studies in Pure Mathematics 59(掲載確定)
  • Peer Reviewed
• [Journal Article] Higher genus Gromov-Witten invariants of the Grassmannian and the Pfaffian Calabi-Yau 3-folds (2009)
  • Author(s): S. Hosono, Y. Konishi
  • Journal Title: Adv.Theor.Math.Phys. Vol. 13 Pages: 463-495
  • Peer Reviewed
• [Journal Article] BCOV rings and holomorphic anomaly equation,to be published in Adv (2009)
  • Author(s): S.Hosono
  • Journal Title: Studies in Pure Math
  • Peer Reviewed
• [Journal Article] Higher genus Gromov-Witten invariants of the Grassmannian and the Pfaffian Calabi-Yau 3-folds Adv. (2009)
  • Author(s): S. Hosono, Y. Konishi
  • Journal Title: Theor. Math. Phys 13 Pages: 463-495
  • Peer Reviewed
• [Journal Article] Higher genus Gromov-Witten invariants of the Grassmannian, and the Pfaffian Calabi-Yau 3-folds (2009)
  • Author(s): S. Hosono and Y. Konishi
  • Journal Title: Adv. Theor. Math. Phys. 13 Pages: 463-495
  • Peer Reviewed
• [Journal Article] On Stokes Matrices of Calabi-Yau Hypersurfaces (2007)
  • Author(s): C. Doran, S. Hosono
  • Journal Title: Adv.Theor.Math.Phys. Vol. 11 Pages: 147-174
  • Peer Reviewed
• [Journal Article] On Stokes Matrices of Calabi-Yau Hypersurfaces Adv. (2007)
  • Author(s): C. Doran, S. Hosono
  • Journal Title: Theor.Math. Phys 11 Pages: 147-174
  • Peer Reviewed
• [Journal Article] On Stokes Matrices of Calabi-Yau Hypersurfaces (2007)
  • Author(s): Charles Doran, Shinobu Hosono
  • Journal Title: Advances in Theoretical and Mathematical Physics 11 Pages: 147-174
  • Peer Reviewed
• [Journal Article] On Stokes matrices of Calabi-Yau hypersurfaces (2007)
  • Author(s): Charles Doram, Shinobu Hosono
  • Journal Title: Advancces in Theoretical Mathematical Physics (To be published)
• [Journal Article] Central Charges, symplectic forms, and hypergeometric series in local mirror symmetry (2006)
  • Author(s): S. Hosono
  • Journal Title: AMS/IP Studies in Adv.Math. Vol. 38 Pages: 405-436
  • Peer Reviewed
• [Journal Article] Central Charges, symplectic forms,and hypergeometric series in local mirror symmetry, AMS/IP Studies in Adv (2006)
  • Author(s): S.Hosono
  • Journal Title: Math 38 Pages: 405-436
  • Peer Reviewed
• [Journal Article] Central Charges, symplectic forms, and hypergeometric series in local mirror symmetry (2006)
  • Author(s): Shinobu Hosono
  • Journal Title: AMS/IP Studies in Advanced Mathematics 38 Pages: 405-436
• [Presentation] 「BCOV ring and holomorphic anomaly equation」, BIRS Workshop "Number theory and physics at the crossroads" (2008)
  • Author(s): 細野忍
  • Organizer: International Conference of Mathematics
  • Place of Presentation: BIRS (Canada)
• [Presentation] BCOV ring, anomaly equation and applications to GW invariants (2008)
  • Author(s): 細野忍
  • Organizer: Workshop on Gromov-Witten theory and related topics
  • Place of Presentation: KIAS (Korea)
• [Presentation] Fourier-Mukai partners and Gromov-Witten invariants (2007)
  • Author(s): 細野忍
  • Organizer: Workshop of Algrbraic Geometry and Physics 2007
  • Place of Presentation: KIAS (Korea)