Mirror maps equal SYZ maps for toric Calabi-Yau surfaces

Details Mirror maps equal SYZ maps for toric Calabi-Yau surfaces Mirror maps equal SYZ maps for toric Calabi-Yau surfaces

2010-08-27

arxiv.org/abs/1008.4753v1

Mathematics

Symplectic Geometry

15 pages, 7 figures

Scientific paper

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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