PreprintCC BY-NC-SA 4.0arXiv
Local Homological Mirror Symmetry
Abstract
Local mirror symmetry, originated from the work of Chiang-Klemm-Yau-Zaslow arXiv:9903053, indicated a potential relation between mirrors to a vector bundle and mirrors to its zero section. In this paper, we constructed a homological mirror to these local varieties and proved the corresponding Homological Mirror Symmetry statement. As an application, we constructed infinite families of exotic Weinstein sectors as mirrors to Hirzebruch surfaces.
Related
- On intrinsic homological mirror symmetry for toric degenerations
- Homological obstructions to local contractibility in noncollapsed Ricci limits
- All genus open mirror symmetry for footballs
- Homological Trimming and Regularity of Filtrations via Local Obstruction Modules
- Landau--Ginzburg mirror symmetry for ADE singularities
BibTeX
@misc{liu2026local,
title = {{Local Homological Mirror Symmetry}},
author = {Si-Yang Liu and Kyungmin Rho},
howpublished = {arXiv},
year = {2026},
month = nov,
doi = {10.48550/arxiv.2611.07202},
eprint = {2611.07202},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2611.07202},
note = {CC BY-NC-SA 4.0},
}
RIS
TY - UNPB
TI - Local Homological Mirror Symmetry
AU - Si-Yang Liu
AU - Kyungmin Rho
PY - 2026
DA - 2026/11/04
PB - arXiv
DO - 10.48550/arxiv.2611.07202
UR - https://arxiv.org/abs/2611.07202
AB - Local mirror symmetry, originated from the work of Chiang-Klemm-Yau-Zaslow arXiv:9903053, indicated a potential relation between mirrors to a vector bundle and mirrors to its zero section. In this paper, we constructed a homological mirror to these local varieties and proved the corresponding Homological Mirror Symmetry statement. As an application, we constructed infinite families of exotic Weinstein sectors as mirrors to Hirzebruch surfaces.
ER -