Lagrangian Floer potential of orbifold spheres

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

Research output: Contribution to journalArticlepeer-review

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

Bibliographical note

Funding Information:
The second author thanks Kyoung-Seog Lee for valuable discussions on the computation of Jacobian ideals. The fourth author expresses his gratitude to Yefeng Shen and Jie Zhou for useful discussions on the mirror maps for elliptic curve quotients. The work of C.H. Cho was supported by the National Research Foundation of Korea (NRF) grant No. 2010-0019516 and by No. 2012R1A1A2003117 . The work of S.-H. Kim was supported by the National Research Foundation of Korea (NRF) grant No. 2013R1A1A1058646 .

Publisher Copyright:
© 2016 Elsevier Inc.

All Science Journal Classification (ASJC) codes

  • Mathematics(all)

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