Mirror maps equal SYZ maps for toric Calabi–Yau surfaces

We prove that the mirror map is the Strominger–Yau–Zaslow map for every toric Calabi–Yau surface. As a consequence, one obtains an enumerative meaning of the mirror map. This involves computing genus‐0 open Gromov–Witten invariants, which is done by relating them with closed Gromov–Witten invariants...

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Bibliographic Details
Published in:The Bulletin of the London Mathematical Society 2012-04, Vol.44 (2), p.255-270
Main Authors: Lau, Siu‐Cheong, Leung, Naichung Conan, Wu, Baosen
Format: Article
Language:English
Online Access:Get full text
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Summary:We prove that the mirror map is the Strominger–Yau–Zaslow map for every toric Calabi–Yau surface. As a consequence, one obtains an enumerative meaning of the mirror map. This involves computing genus‐0 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.
ISSN:0024-6093
1469-2120
DOI:10.1112/blms/bdr090