Lagrangian Floer potential of orbifold spheres

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

doi:10.1016/j.aim.2016.10.017

Lagrangian Floer potential of orbifold spheres

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

Department of Mathematics

Research output: Contribution to journal › Article › peer-review

4 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 language	English
Pages (from-to)	344-426
Number of pages	83
Journal	Advances in Mathematics
Volume	306
DOIs	https://doi.org/10.1016/j.aim.2016.10.017
Publication status	Published - 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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10.1016/j.aim.2016.10.017

Cite this

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title = "Lagrangian Floer potential of orbifold spheres",

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.",

author = "Cho, {Cheol Hyun} and Hansol Hong and Kim, {Sang hyun} and Lau, {Siu Cheong}",

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: {\textcopyright} 2016 Elsevier Inc.",

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AU - Cho, Cheol Hyun

AU - Hong, Hansol

AU - Kim, Sang hyun

AU - Lau, Siu Cheong

N1 - 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.

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N2 - 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.

AB - 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.

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SP - 344

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JO - Advances in Mathematics

JF - Advances in Mathematics

ER -

Lagrangian Floer potential of orbifold spheres

Abstract

Bibliographical note

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