A FORMULA EQUATING OPEN AND CLOSED GROMOV-WITTEN INVARIANTS AND ITS APPLICATIONS TO MIRROR SYMMETRY

摘要

We prove that open Gromov-Witten invariants for semi-Fano toric manifolds of the form X = P(K_Y?O_y), where Y is a tonic Fano manifold, are equal to certain 1-pointed closed Gromov-Witten invariants of X. As applications, we compute the mirror superpotentials for these manifolds. In particular, this gives a simple proof for the formula of the mirror superpotential for the Hirzebruch surface F_2.