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A Hodge module construction of relative Du Bois complexes
Abstract
We construct relative Du Bois and relative intersection Du Bois complexes for smooth-factorizable morphisms to a smooth complex base using relative de Rham complexes of mixed Hodge modules and Grothendieck duality. For a smooth morphism, these complexes recover the relative Kähler differentials. Comparisons with the relative Du Bois complexes of Kovács and Ning remain open. We construct finite filtrations on the absolute Du Bois and intersection Du Bois complexes whose graded pieces are the corresponding relative complexes tensored with differential forms from the base. We also study restriction to fibers and its relation to symbolic m-Du Bois and weak m-rational singularities.
Related
- Relative Du Bois complexes over higher dimensional bases
- Du Bois cohomology of noncommutative spaces and the Hodge numbers invariance conjecture for singular varieties
- Injectivity and vanishing for the Du Bois complexes of isolated singularities
- Mixed Hodge structure in the cohomology of moment-angle complexes
- Vector-Valued Wavelet Bases as Hilbert 𝕄m(ℝ)-Module Bases: A Construction from Scalar Wavelets
BibTeX
@misc{dirks2026hodge,
title = {{A Hodge module construction of relative Du Bois complexes}},
author = {Bradley Dirks},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.17148},
eprint = {2609.17148},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.17148},
}
RIS
TY - UNPB
TI - A Hodge module construction of relative Du Bois complexes
AU - Bradley Dirks
PY - 2026
DA - 2026/09/15
PB - arXiv
DO - 10.48550/arxiv.2609.17148
UR - https://arxiv.org/abs/2609.17148
AB - We construct relative Du Bois and relative intersection Du Bois complexes for smooth-factorizable morphisms to a smooth complex base using relative de Rham complexes of mixed Hodge modules and Grothendieck duality. For a smooth morphism, these complexes recover the relative Kähler differentials. Comparisons with the relative Du Bois complexes of Kovács and Ning remain open. We construct finite filtrations on the absolute Du Bois and intersection Du Bois complexes whose graded pieces are the corresponding relative complexes tensored with differential forms from the base. We also study restriction to fibers and its relation to symbolic m-Du Bois and weak m-rational singularities.
ER -