Extendability of foliations

[2411.04039] Extendability of foliations Skip to main content Search Submit Donate Log in Mathematics > Algebraic Geometry arXiv:2411.04039 (math) [Submitted on 6 Nov 2024 ( v1 ), last revised 25 Aug 2026 (this version, v2)] Title: Extendability of foliations Authors: Pablo Perrella , Sebastián Velazquez View PDF HTML (experimental) Abstract: Given a foliation $\mathcal{F}$ on $X$ and an embedding $X\subseteq Y$, is there a foliation on $Y$ extending $\mathcal{F}$? Using formal methods, we show that this question has an affirmative answer whenever the embedding is sufficiently positive with respect to $(X,\mathcal{F})$ and the singularities of $\mathcal{F}$ belong to a certain class. These tools also apply in the case where $Y$ is the total space of a deformation of $X$. Regarding the uniqueness of the extension, we prove a foliated version of a statement by Fujita and Grauert ensuring the existence of tubular neighborhoods. We also give sufficient conditions for a foliation to have only trivial unfoldings, generalizing a result due to Gómez-Mont. Subjects: Algebraic Geometry (math.AG) MSC classes: 14D15, 14D15, 14D06, 32S65, 32M25 Cite as: arXiv:2411.04039 [math.AG] (or arXiv:2411.04039v2 [math.AG] for this version) https://doi.org/10.48550/arXiv.2411.04039 Focus to learn more arXiv-issued DOI via DataCite Journal reference: Advances in Mathematics, Volume 481, 2025, 110538, ISSN 0001-8708 Related DOI : https://doi.org/10.1016/j.aim.2025.110538 . Focus to learn more DOI(s) linking to related resources Submission history From: Sebastian Lucas Velazquez [ view email ] [v1] Wed, 6 Nov 2024 16:38:58 UTC (37 KB) [v2] Tue, 25 Aug 2026 08:50:25 UTC (35 KB) Full-text links: Access Paper: View PDF HTML (experimental) TeX Source view license Current browse context: math.AG < prev | next > new | recent | 2024-11 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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