Pure and Applied Mathematics Quarterly
Volume 16 (2020)
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
We prove that for a compact toric manifold whose anticanonical divisor is numerically effective, the Lagrangian Floer superpotential defined by Fukaya–Oh–Ohto–Ono  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.
open Gromov–Witten invariant, Lagrangian Floer superpotential, mirror map, toric manifold
2010 Mathematics Subject Classification
Primary 14J33, 53D37. Secondary 14M25, 32S20, 53D12, 53D20, 53D45.
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