Irregular Hodge Bundles for Deligne--Mumford Landau--Ginzburg Families with Fixed Pole Orders
Year: 2026
Type: preprint
Abstract: 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.
Source: arXiv (Cornell University)
Author: Wang, Haoxu
Institution: Academy of Mathematics and Systems Science
Language: English
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7214091385