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Mirror maps equal SYZ maps for toric Calabi–Yau surfaces

Siu-Cheong Lau Boston University Naichung Conan Leung The Chinese University of Hong Kong Baosen Wu Tsinghua University

mathscidoc:1702.01010

Bull. London Math. Soc., 44, (44), 255-270, 2012
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.
mirror map, SYZ, toric Calabi-Yau, A_n resolution
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@inproceedings{siu-cheong2012mirror,
  title={Mirror maps equal SYZ maps for toric Calabi–Yau surfaces},
  author={Siu-Cheong Lau, Naichung Conan Leung, and Baosen Wu},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20170213235610522138437},
  booktitle={Bull. London Math. Soc.},
  volume={44},
  number={44},
  pages={255-270},
  year={2012},
}
Siu-Cheong Lau, Naichung Conan Leung, and Baosen Wu. Mirror maps equal SYZ maps for toric Calabi–Yau surfaces. 2012. Vol. 44. In Bull. London Math. Soc.. pp.255-270. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20170213235610522138437.
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