Global structure of mirror symmetry

2015 Fiscal Year Final Research Report

• Project/Area Number: 25400069
• Research Category: Grant-in-Aid for Scientific Research (C)
• Allocation Type: Multi-year Fund
• Section: 一般
• Research Field: Geometry
• Research Institution: Kyoto University
• Principal Investigator: Iritani Hiroshi 京都大学, 理学(系)研究科(研究院), 准教授 (20448400)
• Project Period (FY): 2013-04-01 – 2016-03-31
• Keywords: 量子コホモロジー / グロモフ・ウィッテン理論 / ミラー対称性 / トーリック多様体 / ランダウ・ギンズブルグ模型 / 軌道体 / ファノ多様体 / 導来圏

Outline of Final Research Achievements

We studied Gromov-Witten theory through global mirror symmetry. More concretely, (1) we proved a mirror theorem for complete intersections in toric orbifolds with Coates, Corti and Tseng; (2) we proved the crepant transformation conjecture for these spaces and showed that it is related to equivalences between derived categories of coherent sheaves with Coates and Jiang; (3) we constructed a theory of Fock sheaves for higher genus theory and showed a certain modularity of the potential with Coates; (4) we formulated Gamma conjecture for Fano manifolds with Galkin and Golyshev. We also obtained results on quantum K-theory, quantum Serre duality and a relationship between extremal transitions and quantum cohomology.

Free Research Field

幾何学