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)

Abstract

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
Volume306
DOIs
Publication statusPublished - 2017 Jan 14

Fingerprint

Orbifold
Mirror
Mirror Symmetry
Isolated Singularity
Infinite series
Elliptic Curves
Quotient
Meaning
Class

All Science Journal Classification (ASJC) codes

  • Mathematics(all)

Cite this

Cho, Cheol Hyun ; Hong, Hansol ; Kim, Sang hyun ; Lau, Siu Cheong. / Lagrangian Floer potential of orbifold spheres. In: Advances in Mathematics. 2017 ; Vol. 306. pp. 344-426.
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Lagrangian Floer potential of orbifold spheres. / Cho, Cheol Hyun; Hong, Hansol; Kim, Sang hyun; Lau, Siu Cheong.

In: Advances in Mathematics, Vol. 306, 14.01.2017, p. 344-426.

Research output: Contribution to journalArticle

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