Lagrangian Floer potential of orbifold spheres

Cheol Hyun Cho, Hansol Hong, Sang hyun Kim, Siu Cheong Lau

Research output: Contribution to journalArticle

3 Citations (Scopus)


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.

Original languageEnglish
Pages (from-to)344-426
Number of pages83
JournalAdvances in Mathematics
Publication statusPublished - 2017 Jan 14

All Science Journal Classification (ASJC) codes

  • Mathematics(all)

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