Local Calabi–Yau manifolds of type A˜ via SYZ mirror symmetry
Files
Accepted manuscript
Date
2019-05
Authors
Lau, Siu
Kanazawa, Atsushi
Version
Accepted manuscript
OA Version
Citation
Atsushi Kanazawa, Siu Lau. "Local Calabi-Yau manifolds of affine type A˜ via SYZ mirror symmetry." Journal of Geometry and Physics, Volume 139, May 2019, Pages 103-138. https://doi.org/10.1016/j.geomphys.2018.12.015
Abstract
We carry out the SYZ program for the local Calabi–Yau manifolds of type A˜ by developing an equivariant SYZ theory for the toric Calabi–Yau manifolds of infinite-type. Mirror geometry is shown to be expressed in terms of the Riemann theta functions and generating functions of open Gromov–Witten invariants, whose modular properties are found and studied in this article. Our work also provides a mathematical justification for a mirror symmetry assertion of the physicists Hollowood–Iqbal–Vafa (Hollowood et al., 2008).