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

Abstract

We prove that for a compact toric manifold whose anti-canonical 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.

arXiv commentv3: 32 pages, 1 figure. Dedicated to Prof. K. Saito on the occasion of his 75th birthday