Lagrangian Floer potential of orbifold spheres

Cheol-Hyun Cho Seoul National University Hansol Hong Harvard University Sang-Hyun Kim Seoul National University Siu-Cheong Lau Boston University


Adv. Math., 306, 344-426, 2017
For each sphere with three orbifold points, we construct an algorithm to compute the open Gromov-Witten potential, which serves as the quantum-corrected Landau-Ginzburg mirror and is an infinite series in general. This gives the first class of general-type geometries whose full potentials can be computed. As a consequence we obtain an enumerative meaning of mirror maps for elliptic curve quotients. Furthermore, we prove that the open Gromov-Witten potential is convergent, even in the general-type cases, and has an isolated singularity at the origin, which is an important ingredient of proving homological mirror symmetry.
SYZ, mirror symmetry, orbifold, elliptic, hyperbolic, Lagrangian Floer, potential
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  title={Lagrangian Floer potential of orbifold spheres},
  author={Cheol-Hyun Cho, Hansol Hong, Sang-Hyun Kim, and Siu-Cheong Lau},
  booktitle={Adv. Math.},
Cheol-Hyun Cho, Hansol Hong, Sang-Hyun Kim, and Siu-Cheong Lau. Lagrangian Floer potential of orbifold spheres. 2017. Vol. 306. In Adv. Math.. pp.344-426.
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