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Calculating Hodge and weight filtrations on localizations
Abstract
We describe the Macaulay2 package MixedHodgeModules, which computes Hodge and weight filtrations on localizations S_f of a polynomial ring S at a non-constant reduced polynomial f, as well as on twisted localizations S_f f^{-α}, where α\in QQ is rational. The package includes functionality for computing Hodge ideals, weighted Hodge ideals, higher multiplier ideals, generation levels of Hodge filtrations, weight levels of elements, p-functions, and lengths of weight filtrations. It also provides routines for computing graded de Rham complexes, Du Bois complexes, and intersection Du Bois complexes of hypersurfaces.
Related
- F-nilpotence and Hodge filtrations beyond isolated singularities
- Simpson filtrations and closure relations of Hodge moduli spaces
- Almost Gorenstein standard graded rings and their localizations
- Presentability of categories of localizations and analytic rings
- Isotropic localizations of mixed initial motives
BibTeX
@misc{lorincz2026calculating,
title = {{Calculating Hodge and weight filtrations on localizations}},
author = {András C. Lőrincz and Michael Perlman},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.36180},
eprint = {2609.36180},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.36180},
}
RIS
TY - UNPB
TI - Calculating Hodge and weight filtrations on localizations
AU - András C. Lőrincz
AU - Michael Perlman
PY - 2026
DA - 2026/09/28
PB - arXiv
DO - 10.48550/arxiv.2609.36180
UR - https://arxiv.org/abs/2609.36180
AB - We describe the Macaulay2 package MixedHodgeModules, which computes Hodge and weight filtrations on localizations S_f of a polynomial ring S at a non-constant reduced polynomial f, as well as on twisted localizations S_f f^{-α}, where α\in QQ is rational. The package includes functionality for computing Hodge ideals, weighted Hodge ideals, higher multiplier ideals, generation levels of Hodge filtrations, weight levels of elements, p-functions, and lengths of weight filtrations. It also provides routines for computing graded de Rham complexes, Du Bois complexes, and intersection Du Bois complexes of hypersurfaces.
ER -