Irregular Hodge Bundles for Deligne--Mumford Landau--Ginzburg Families with Fixed Pole Orders

@misc{wang2026irregular,
  title = {{Irregular Hodge Bundles for Deligne--Mumford Landau--Ginzburg Families with Fixed Pole Orders}},
  author = {Haoxu Wang},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.26239},
  eprint = {2609.26239},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.26239},
}

TY  - UNPB
TI  - Irregular Hodge Bundles for Deligne--Mumford Landau--Ginzburg Families with Fixed Pole Orders
AU  - Haoxu Wang
PY  - 2026
DA  - 2026/09/01
PB  - arXiv
DO  - 10.48550/arxiv.2609.26239
UR  - https://arxiv.org/abs/2609.26239
AB  - We prove that the canonical irregular Hodge filtrations in smooth families of Deligne--Mumford Landau--Ginzburg models with fixed pole orders assemble into filtered algebraic vector bundles. More precisely, twisted de Rham cohomology forms a vector bundle carrying a canonical algebraic integrable connection, every rational irregular Hodge level is a subbundle with locally free quotient, and every rational graded piece is a vector bundle. These constructions commute with arbitrary finite-type base change, and the connection satisfies shifted Griffiths transversality. Consequently, all filtered and graded dimensions are locally constant. As an application, for a smooth quasiprojective toric Deligne--Mumford stack and every fixed Newton polytope at infinity satisfying the support condition, these conclusions hold over the full coefficient locus of Laurent polynomials that are nondegenerate at infinity. In particular, their filtered and graded dimensions are independent of the coefficients. When the resulting stacky fans form a Clarke dual pair, the irregular Hodge numbers are computed by Harder--Lee's combinatorial Ξ-complex.
ER  -