Mirror maps equal SYZ maps for toric Calabi-Yau surfaces
Siu-Cheong Lau, Naichung Conan Leung, Baosen Wu
TL;DR
This paper proves that for toric Calabi-Yau surfaces, the mirror map coincides with the SYZ map, providing an enumerative interpretation through genus-zero open Gromov-Witten invariants and their relation to closed invariants.
Contribution
It establishes the equality of mirror and SYZ maps for toric Calabi-Yau surfaces and links open Gromov-Witten invariants to closed invariants for enumerative geometry.
Findings
Mirror map equals SYZ map for toric Calabi-Yau surfaces
Provides enumerative meaning of the mirror map
Relates open and closed Gromov-Witten invariants
Abstract
We prove that the mirror map is the SYZ map for every toric Calabi-Yau surface. As a consequence one obtains an enumerative meaning of the mirror map. This involves computing genus-zero open Gromov-Witten invariants, which is done by relating them with closed Gromov-Witten invariants via compactification and using an earlier computation by Bryan-Leung.
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