Moduli and peiods for Landau-Ginzburg models

2020 Fiscal Year Final Research Report

• Project/Area Number: 19K21021
• Project/Area Number (Other): 18H05829 (2018)
• Research Category: Grant-in-Aid for Research Activity Start-up
• Allocation Type: Multi-year Fund (2019); Single-year Grants (2018)
• Review Section: 0201:Algebra, geometry, analysis, applied mathematics,and related fields
• Research Institution: The University of Tokyo
• Principal Investigator: Shamoto Yota 東京大学, カブリ数物連携宇宙研究機構, 特任研究員 (50823647)
• Project Period (FY): 2018-08-24 – 2021-03-31
• Keywords: ミラー対称性 / Landau-Ginzburg model / 周期積分

Outline of Final Research Achievements

We have studied a geometric object, called a Landau-Ginzburg (LG) model, which consists of an algebraic variety and a regular function on it, and its period integral. The main source of idea is the mirror symmetry conjecture, which relates LG model with Fano manifolds. The main results are, 1. a preprint on an algebraic structure of exponential type vertex operators, which closely related to exponential period. 2. a preprint on the Stokes structure for differential-difference modules obtained from the period integral for LG models which should correspond to equivariant quantum cohomology groups for Fano manifolds.

Free Research Field

複素幾何学

Academic Significance and Societal Importance of the Research Achievements

本研究は, 数理物理学におけるミラー対称性や共形場理論のアイデアに基づく数学的構造の研究であるため, その進展, 理解の深まりは, これらの理論に対するより明確な理解につながると考えている. さらに, 差分方程式と呼ばれる離散的な対象に対する代数的なStokes構造の理論を確立することは, 学術的な意義もあると考えている.