Gross fibration, SYZ mirror symmetry, and open Gromov-Witten invariants for toric Calabi-Yau orbifolds

Abstract

Given a toric Calabi-Yau orbifold X, we define and study a non-toric Lagrangian torus fibration on X, which we call the Gross fibration. We apply the SYZ recipe to a suitable modification of the Gross fibration of X to construct an instanton-corrected mirror of X. To further study the instanton corrections, we explicitly evaluate all relevant open Gromov- Witten invariants of X via an open/closed equality and mirror theorem for toric orbifolds. We apply our calculations to study relations between open Gromov-Witten invariants and periods of the mirror, and to prove a result on how open Gromov-Witten invariants change under toric crepant resolutions