Period integrals, mirror symmetry, and the geometry of Gromov-Witten invariants

2014 Fiscal Year Final Research Report

• Project/Area Number: 22540041
• 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 東京大学, 数理(科)学研究科(研究院), 准教授 (60212198)
• Project Period (FY): 2010-04-01 – 2015-03-31
• Keywords: カラビ・ヤウ多様体 / ミラー対称性 / 導来圏 / グロモフ･ウィッテン不変量 / 周期積分 / 射影幾何学

Outline of Final Research Achievements

Mirror symmetry of Calabi-Yau manifolds is a mysterious symmetry which has been found in the study of string theory in theoretical physics. Since its discovery, mirror symmetry has been studied in major institutes in the world. In this research, we have focused on Calabi-Yau manifolds which are called Reye congruence in the language of classical projective geometry. Finding a mirror Calabi-Yau manifold of Reye congruence Calabi-Yau manifold, and studying its deformation family, we have found that there appears another Calabi-Yau manifold which is paired with the Reye congruence. We have shown that this pair arises naturally from the projective duality. Furthermore, from a more modern viewpoint, we have shown that the two Calabi-Yau manifolds share an equivalent derived category of coherent sheaves. Interesting interplay between the projective duality and mirror symmetry has been appeared from this research.

Free Research Field

数理物理学･代数学