Gross fibration, SYZ mirror symmetry, and open Gromov-Witten invariants for toric Calabi-Yau orbifolds
Files
Accepted manuscript
Date
2016
DOI
Authors
Lau, Siu-Cheong
Chan, Kwokwai
Cho, Cheol-Hyun
Tseng, Hsian-Hua
Version
OA Version
Citation
SC Lau. 2016. "Gross fibration, SYZ mirror symmetry, and open Gromov-Witten invariants for toric Calabi-Yau orbifolds." Journal of Differential Geometry,
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.