Compactification Independence of the Irregular Hodge Filtration on Deligne-Mumford Stacks
Abstract
Let (π°,w) be a smooth separated Deligne--Mumford stack of finite type over β, with a regular function w. Following Yu, one can use a compactification to define a filtration on its twisted de Rham cohomology. The same compactification gives Kontsevich lattices that compute this filtration. The extension of w on the compactification may be only rational. Only a local nondegeneracy condition near the polar divisor is imposed. We prove that the resulting filtration does not depend on the compactification. The proof uses good resolutions and stacky weak factorization. This reduces the comparison to blowups and roots along boundary divisors. Filtered comparison theorems for the Yu and Kontsevich complexes are established for both operations. Harder and Lee use orbifold irregular Hodge numbers in their study of stacky Clarke mirror pairs. Compactification independence applies sector by sector to their setting. Thus the resulting orbifold filtration and irregular Hodge numbers depend only on the stack Landau--Ginzburg model.
Related
- Irregular Hodge Bundles for Deligne--Mumford Landau--Ginzburg Families with Fixed Pole Orders
- Existence of coarse moduli superspaces for Deligne--Mumford superstacks
- A Quadratically Enriched Pushforward for Deligne--Mumford Stacks
- Torelli Theorem for moduli stacks of vector bundles on tame Deligne Mumford curves
- Equivariant principal bundles over toric Deligne--Mumford stacks
BibTeX
@misc{wang2026compactification,
title = {{Compactification Independence of the Irregular Hodge Filtration on Deligne-Mumford Stacks}},
author = {Haoxu Wang},
howpublished = {arXiv},
year = {2026},
month = aug,
doi = {10.48550/arxiv.2608.06234},
eprint = {2608.06234},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2608.06234},
}
RIS
TY - UNPB
TI - Compactification Independence of the Irregular Hodge Filtration on Deligne-Mumford Stacks
AU - Haoxu Wang
PY - 2026
DA - 2026/08/28
PB - arXiv
DO - 10.48550/arxiv.2608.06234
UR - https://arxiv.org/abs/2608.06234
AB - Let (π°,w) be a smooth separated Deligne--Mumford stack of finite type over β, with a regular function w. Following Yu, one can use a compactification to define a filtration on its twisted de Rham cohomology. The same compactification gives Kontsevich lattices that compute this filtration. The extension of w on the compactification may be only rational. Only a local nondegeneracy condition near the polar divisor is imposed. We prove that the resulting filtration does not depend on the compactification. The proof uses good resolutions and stacky weak factorization. This reduces the comparison to blowups and roots along boundary divisors. Filtered comparison theorems for the Yu and Kontsevich complexes are established for both operations. Harder and Lee use orbifold irregular Hodge numbers in their study of stacky Clarke mirror pairs. Compactification independence applies sector by sector to their setting. Thus the resulting orbifold filtration and irregular Hodge numbers depend only on the stack Landau--Ginzburg model.
ER -