Lagrangian Floer potential of orbifold spheres
MetadataShow full item record
Citation (published version)Cheol-Hyun Cho, Hansol Hong, Sang-hyun Kim, Siu-Cheong Lau. 2017. "Lagrangian Floer potential of orbifold spheres." Advances in Mathematics, v. 306, pp. 344 - 426. https://doi.org/10.1016/j.aim.2016.10.017
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.