Pure and Applied Mathematics Quarterly

Volume 16 (2020)

Number 3

Special Issue: In Honor of Prof. Kyoji Saito’s 75th Birthday

Guest Editors: Stanislaw Janeczko, Si Li, Jie Xiao, Stephen S.T. Yau, and Huaiqing Zuo

Open Gromov–Witten invariants and mirror maps for semi-Fano toric manifolds

Pages: 675 – 720

DOI: https://dx.doi.org/10.4310/PAMQ.2020.v16.n3.a11

Authors

Kwokwai Chan (Department of Mathematics, Chinese University of Hong Kong, Shatin, Hong Kong)

Siu-Cheong Lau (Department of Mathematics and Statistics, Boston University, Boston, Massachusetts, U.S.A.)

Naichung Conan Leung (Institute of Mathematical Sciences and Department of Mathematics, Chinese University of Hong Kong, Shatin, Hong Kong)

Hsian-Hua Tseng (Department of Mathematics, Ohio State University, Columbus, Oh., U.S.A.)

Abstract

We prove that for a compact toric manifold whose anticanonical divisor is numerically effective, the Lagrangian Floer superpotential defined by Fukaya–Oh–Ohto–Ono [15] is equal to the superpotential written down by using the toric mirror map under a convergence assumption. This gives a method to compute open Gromov–Witten invariants using mirror symmetry.

Keywords

open Gromov–Witten invariant, Lagrangian Floer superpotential, mirror map, toric manifold

2010 Mathematics Subject Classification

Primary 14J33, 53D37. Secondary 14M25, 32S20, 53D12, 53D20, 53D45.

Full Text (PDF format)

The work of K. C. was supported in part by a grant from the Hong Kong Research Grants Council (Project No. CUHK404412). The work of S.-C. L. was supported by IPMU and Harvard University. The work of N. C. L. was supported by a grant from the Hong Kong Research Grants Council (Project No. CUHK401809). The work of H.-H. T. was supported in part by NSF grant DMS-1047777.

Received 30 January 2019

Accepted 2 April 2020

Published 11 November 2020