Mirror maps equal SYZ maps for toric Calabi-Yau surfaces
classification
🧮 math.SG
math.AG
keywords
mirrorcalabi-yaugromov-witteninvariantsmapstoricbryan-leungclosed
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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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