Nonrationality Degree of Toric Quasifolds

[2607.10220] Nonrationality Degree of Toric Quasifolds Skip to main content Search Submit Donate Log in Mathematics > Algebraic Geometry arXiv:2607.10220 (math) [Submitted on 11 Jul 2026 ( v1 ), last revised 15 Aug 2026 (this version, v2)] Title: Nonrationality Degree of Toric Quasifolds Authors: Fiammetta Battaglia , Elisa Prato View PDF HTML (experimental) Abstract: Toric quasifolds are nonrational generalizations of toric manifolds and orbifolds. We introduce the notion of nonrationality degree, an invariant that measures the extent to which a toric quasifold fails to be Hausdorff. We do so by first defining analogous notions for the underlying quasilattice and the corresponding quasitorus. We conclude by applying the nonrationality degree to reframe Gordan's lemma in the nonrational setting. Comments: 14 pages, minor revisions and updated references Subjects: Algebraic Geometry (math.AG) ; Differential Geometry (math.DG); Symplectic Geometry (math.SG) MSC classes: Primary: 14M25. Secondary: 52B20 Cite as: arXiv:2607.10220 [math.AG] (or arXiv:2607.10220v2 [math.AG] for this version) https://doi.org/10.48550/arXiv.2607.10220 Focus to learn more arXiv-issued DOI via DataCite Journal reference: Mathematics 2026, 14(17), 3028 Related DOI : https://doi.org/10.3390/math14173028 Focus to learn more DOI(s) linking to related resources Submission history From: Elisa Prato [ view email ] [v1] Sat, 11 Jul 2026 09:20:16 UTC (12 KB) [v2] Sat, 15 Aug 2026 16:00:24 UTC (13 KB) Full-text links: Access Paper: View PDF HTML (experimental) TeX Source view license Current browse context: math.AG < prev | next > new | recent | 2026-07 Change to browse by: math math.DG math.SG 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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