Open Gromov-Witten invariants and SYZ under local conifold transitions

Abstract

For a local Calabi-Yau manifold which is a smoothing of toric Gorenstein singularity, this paper computes the open Gromov-Witten invariants of a generic fiber of the special Lagrangian fibration constructed by Gross and thereby constructs its SYZ mirror. Moreover it derives a relation for the generating function of open Gromov-Witten invariants of the local Calabi-Yau manifold and that of its conifold transition.