Stringy Irregular Hodge Numbers for Non-Simplicial Toric Landau--Ginzburg Data
Abstract
We extend orbifold irregular Hodge theory from simplicial toric Landau--Ginzburg models to data defined by possibly non-simplicial stacky fans. For a Clarke mirror pair, we construct a filtered Koszul--de Rham complex over toric face rings. For simplicial ray-supported data, a strict filtered comparison identifies this complex with the Harder--Lee cellular residue complex, and hence it computes the orbifold irregular Hodge numbers. Using this complex, for a fixed possibly non-simplicial datum, we prove that the models obtained from its projective crepant simplicial subdivisions have the same orbifold irregular Hodge polynomial whenever the potential is nondegenerate at infinity. This common value defines the stringy irregular Hodge numbers of the original datum.
Related
- Irregular Hodge Bundles for Deligne--Mumford Landau--Ginzburg Families with Fixed Pole Orders
- 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
- Landau--Ginzburg mirror symmetry for ADE singularities
- Global minimality of the degree-one Ginzburg-Landau vortex solution in the unit ball in dimensions n ≥ 2
BibTeX
@misc{wang2026stringy,
title = {{Stringy Irregular Hodge Numbers for Non-Simplicial Toric Landau--Ginzburg Data}},
author = {Haoxu Wang},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.29579},
eprint = {2609.29579},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.29579},
}
RIS
TY - UNPB
TI - Stringy Irregular Hodge Numbers for Non-Simplicial Toric Landau--Ginzburg Data
AU - Haoxu Wang
PY - 2026
DA - 2026/09/01
PB - arXiv
DO - 10.48550/arxiv.2609.29579
UR - https://arxiv.org/abs/2609.29579
AB - We extend orbifold irregular Hodge theory from simplicial toric Landau--Ginzburg models to data defined by possibly non-simplicial stacky fans. For a Clarke mirror pair, we construct a filtered Koszul--de Rham complex over toric face rings. For simplicial ray-supported data, a strict filtered comparison identifies this complex with the Harder--Lee cellular residue complex, and hence it computes the orbifold irregular Hodge numbers. Using this complex, for a fixed possibly non-simplicial datum, we prove that the models obtained from its projective crepant simplicial subdivisions have the same orbifold irregular Hodge polynomial whenever the potential is nondegenerate at infinity. This common value defines the stringy irregular Hodge numbers of the original datum.
ER -