Open Gromov-Witten invariants and superpotentials for semi-Fano toric surfaces

Kwokwai Chan The Chinese University of Hong Kong Siu-Cheong Lau Boston University

mathscidoc:1702.01011

Int Math Res Notices, 3759-3789, 2013
We compute the open Gromov-Witten invariants for every compact semi-Fano toric surface, i.e. a toric surface X with nef anticanonical bundle. Unlike the Fano case, this involves non-trivial obstructions in the corresponding moduli problem. As an application, an explicit expression of the superpotential W for the mirror of X is obtained, which in turn gives an explicit ring presentation of the small quantum cohomology of X. We also give a computational verification of the natural ring isomorphism between the small quantum cohomology of X and the Jacobian ring of W.
Mirror symmetry, mirror map, open Gromov-Witten, SYZ, toric
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@inproceedings{kwokwai2013open,
  title={Open Gromov-Witten invariants and superpotentials for semi-Fano toric surfaces},
  author={Kwokwai Chan, and Siu-Cheong Lau},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20170214000055490813438},
  booktitle={Int Math Res Notices},
  pages={3759-3789},
  year={2013},
}
Kwokwai Chan, and Siu-Cheong Lau. Open Gromov-Witten invariants and superpotentials for semi-Fano toric surfaces. 2013. In Int Math Res Notices. pp.3759-3789. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20170214000055490813438.
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