Kähler thresholds

[2606.08224] Kähler thresholds Skip to main content Search Submit Donate Log in Mathematics > Algebraic Geometry arXiv:2606.08224 (math) [Submitted on 6 Jun 2026 ( v1 ), last revised 27 Aug 2026 (this version, v2)] Title: Kähler thresholds Authors: Gabriella Clemente , Carlos Simpson View PDF HTML (experimental) Abstract: The topology of Kähler manifolds is largely determined by the geometry due to its rigidity. In particular, the cohomology and Hodge theory of compact Kähler manifolds is quite restricted. We prove that within a certain threshold, the odd Betti numbers of any compact almost-hermitian manifold satisfying a degenerate Kähler condition are even, and the even Betti numbers are strictly positive. We call this new type of degenerated Kähler manifold acK. Our approach to proving these results makes use of a compactness theorem for acK manifolds, and a new version of Hodge theory for compact manifolds endowed with a Sobolev regular Kähler strucutre. In addition, we lay out a program to pursue the study of acK geometry that accommodates not only the classical viewpoint, but also constructive and finitary proofs, as well as formalization with proof assistants. Comments: Minor corrections Subjects: Algebraic Geometry (math.AG) ; Complex Variables (math.CV); Differential Geometry (math.DG) Cite as: arXiv:2606.08224 [math.AG] (or arXiv:2606.08224v2 [math.AG] for this version) https://doi.org/10.48550/arXiv.2606.08224 Focus to learn more arXiv-issued DOI via DataCite Submission history From: Carlos Simpson [ view email ] [v1] Sat, 6 Jun 2026 15:26:54 UTC (28 KB) [v2] Thu, 27 Aug 2026 20:47:45 UTC (28 KB) Full-text links: Access Paper: View PDF HTML (experimental) TeX Source view license Current browse context: math.AG < prev | next > new | recent | 2026-06 Change to browse by: math math.CV math.DG 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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