PreprintCC BY 4.0arXiv
Landau--Ginzburg mirror symmetry for ADE singularities
Abstract
We prove Landau-Ginzburg mirror symmetry conjecture for ADE singularities with the nontrivial symmetry groups. In particular, we consider (f,G) with f ∈ ℂ[z1,z2,z3] defining ADE singularity and G --- nontrivial group of diagonal symmetries of f. We show that orbifold Saito theory of (f,G) is isomorphic to the Fan-Jarvis-Ruan-Witten theory of its Berglund-Hübsch-Henningson dual pair (f̃, G̃).
Related
- Motivic Vanishing Cycles at Infinity and Toric Landau-Ginzburg Mirror Symmetry
- Existence of weak Landau-Ginzburg models for weighted complete intersections
- Topological defect trains excited by a boundary discontinuity in the two-dimensional complex Ginzburg-Landau equation
- Global minimality of the degree-one Ginzburg-Landau vortex solution in the unit ball in dimensions n ≥ 2
- The stochastic Ginzburg-Landau equation with harmonic potential in the full subcritical regime
BibTeX
@misc{basalaev2026landauginzburg,
title = {{Landau--Ginzburg mirror symmetry for ADE singularities}},
author = {Alexey Basalaev},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.33442},
eprint = {2609.33442},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.33442},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Landau--Ginzburg mirror symmetry for ADE singularities
AU - Alexey Basalaev
PY - 2026
DA - 2026/09/27
PB - arXiv
DO - 10.48550/arxiv.2609.33442
UR - https://arxiv.org/abs/2609.33442
AB - We prove Landau-Ginzburg mirror symmetry conjecture for ADE singularities with the nontrivial symmetry groups. In particular, we consider (f,G) with f ∈ ℂ[z_1,z_2,z_3] defining ADE singularity and G --- nontrivial group of diagonal symmetries of f. We show that orbifold Saito theory of (f,G) is isomorphic to the Fan-Jarvis-Ruan-Witten theory of its Berglund-Hübsch-Henningson dual pair (f̃, G̃).
ER -