Relative Gromov–Witten invariants and the enumerative meaning of mirror maps for toric Calabi–Yau orbifolds

Abstract

We provide an enumerative meaning of the mirror maps for toric Calabi–Yau orbifolds in terms of relative Gromov–Witten invariants of the toric compactifications. As a consequence, we obtain an equality between relative Gromov–Witten invariants and open Gromov–Witten invariants. Therefore, the instanton corrected mirrors for toric Calabi–Yau orbifolds can be constructed using relative Gromov–Witten invariants.