# MathSciDoc: An Archive for Mathematician ∫

#### Distinguished Paper Award in 2017

Journal of Differential Geometry
This paper gives a new way of constructing Landau-Ginzburg mirrors using deformation theory of Lagrangian immersions motivated by the works of Seidel, Strominger-Yau-Zaslow and Fukaya-Oh-Ohta-Ono. Moreover we construct a canonical functor from the Fukaya category to the mirror category of matrix factorizations. This functor derives homological mirror symmetry under some explicit assumptions. As an application, the construction is applied to spheres with three orbifold points to produce their quantum-corrected mirrors and derive homological mirror symmetry. Furthermore we discover an enumerative meaning of the (inverse) mirror map for elliptic curve quotients.
mirror symmetry, SYZ, orbifold projective line, Lagrangian Floer theory, matrix factorization
```@inproceedings{cheol-hyunlocalized,
title={Localized mirror functor for Lagrangian immersions, and homological mirror symmetry for \$\mathbb{P}^1_{a,b,c}\$},
author={Cheol-Hyun Cho, Hansol Hong, and Siu-Cheong Lau},
url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20160525101152699991036},
booktitle={Journal of Differential Geometry},
}
```
Cheol-Hyun Cho, Hansol Hong, and Siu-Cheong Lau. Localized mirror functor for Lagrangian immersions, and homological mirror symmetry for \$\mathbb{P}^1_{a,b,c}\$. In Journal of Differential Geometry. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20160525101152699991036.