Compactification Independence of the Irregular Hodge Filtration on Deligne-Mumford Stacks

[2608.06234] Compactification Independence of the Irregular Hodge Filtration on Deligne-Mumford Stacks Skip to main content Search Submit Donate Log in Mathematics > Algebraic Geometry arXiv:2608.06234 (math) [Submitted on 6 Aug 2026 ( v1 ), last revised 28 Aug 2026 (this version, v2)] Title: Compactification Independence of the Irregular Hodge Filtration on Deligne-Mumford Stacks Authors: Haoxu Wang View PDF HTML (experimental) Abstract: Let $(\mathscr U,w)$ be a smooth separated Deligne--Mumford stack of finite type over $\mathbb C$, 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. Comments: 37 pages. Substantially revised version; notation standardized, arguments and exposition clarified Subjects: Algebraic Geometry (math.AG) MSC classes: 14F40, 14A20, 14E05, 14J33 Cite as: arXiv:2608.06234 [math.AG] (or arXiv:2608.06234v2 [math.AG] for this version) https://doi.org/10.48550/arXiv.2608.06234 Focus to learn more arXiv-issued DOI via DataCite Submission history From: Haoxu Wang [ view email ] [v1] Thu, 6 Aug 2026 16:20:54 UTC (44 KB) [v2] Fri, 28 Aug 2026 05:49:08 UTC (46 KB) Full-text links: Access Paper: View PDF HTML (experimental) TeX Source view license Current browse context: math.AG < prev | next > new | recent | 2026-08 Change to browse by: math References & Citations SciX Google Scholar Semantic Scholar export BibTeX citation Bookmark Bibliographic Tools Bibliographic and Citation Tools Bibliographic Explorer Toggle Bibliographic Explorer ( What is the Explorer? ) Connected Papers Toggle Connected Papers ( What is Connected Papers? ) Litmaps Toggle Litmaps ( What is Litmaps? ) scite.ai Toggle scite Smart Citations ( What are Smart Citations? ) Code, Data, Media Code, Data and Media Associated with this Article alphaXiv Toggle alphaXiv ( What is alphaXiv? ) Links to Code Toggle CatalyzeX Code Finder for Papers ( What is CatalyzeX? ) DagsHub Toggle DagsHub ( What is DagsHub? ) GotitPub Toggle Gotit.pub ( What is GotitPub? ) Huggingface Toggle Hugging Face ( What is Huggingface? ) ScienceCast Toggle ScienceCast ( What is ScienceCast? ) Demos Demos Replicate Toggle Replicate ( What is Replicate? ) Spaces Toggle Hugging Face Spaces ( What is Spaces? ) Spaces Toggle TXYZ.AI ( What is TXYZ.AI? ) Related Papers Recommenders and Search Tools Link to Influence Flower Influence Flower ( What are Influence Flowers? ) Core recommender toggle CORE Recommender ( What is CORE? ) Author Venue Institution Topic About arXivLabs arXivLabs: experimental projects with community collaborators arXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website. Both individuals and organizations that work with arXivLabs have embraced and accepted our values of openness, community, excellence, and user data privacy. arXiv is committed to these values and only works with partners that adhere to them. Have an idea for a project that will add value for arXiv's community? Learn more about arXivLabs . Which authors of this paper are endorsers? | Disable MathJax ( What is MathJax? ) We gratefully acknowledge support from our major funders , member institutions , and all contributors. About · Help · Contact · Subscribe · Copyright · Privacy · Accessibility · Operational Status (opens in new tab)

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