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Mirror maps equal SYZ maps for toric Calabi-Yau surfaces (1008.4753v2)
Published 27 Aug 2010 in math.SG and math.AG
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.