On Hodge structures of compact complex manifolds with semistable degenerations

[2405.01291] On Hodge structures of compact complex manifolds with semistable degenerations Skip to main content Search Submit Donate Log in Search arXiv Press Enter to search · Advanced search Mathematics > Algebraic Geometry arXiv:2405.01291 (math) [Submitted on 2 May 2024 ( v1 ), last revised 10 Apr 2026 (this version, v4)] Title: On Hodge structures of compact complex manifolds with semistable degenerations Authors: Taro Sano View a PDF of the paper titled On Hodge structures of compact complex manifolds with semistable degenerations, by Taro Sano View PDF HTML (experimental) Abstract: Compact Kähler manifolds satisfy several nice Hodge-theoretic properties such as the Hodge symmetry, the Hard Lefschetz property and the Hodge-Riemann bilinear relations, etc. In this note, we investigate when such nice properties hold on compact complex manifolds with semistable degenerations. For compact complex manifolds which can be obtained as smoothings of SNC varieties without triple intersection locus, we show the Hodge symmetry when the monodromy logarithm induces isomorphisms on the associated graded pieces of the weight filtrations of the limiting mixed Hodge structures. We also show the Hodge-Riemann relations on H^3 of compact complex 3-folds with such semistable degenerations under some conditions. Comments: 25 pages, to appear in Math. Z Subjects: Algebraic Geometry (math.AG) Cite as: arXiv:2405.01291 [math.AG] (or arXiv:2405.01291v4 [math.AG] for this version) https://doi.org/10.48550/arXiv.2405.01291 Focus to learn more arXiv-issued DOI via DataCite Submission history From: Taro Sano [ view email ] [v1] Thu, 2 May 2024 13:53:55 UTC (20 KB) [v2] Tue, 14 May 2024 08:57:05 UTC (24 KB) [v3] Thu, 30 May 2024 07:44:08 UTC (25 KB) [v4] Fri, 10 Apr 2026 07:58:50 UTC (29 KB) Full-text links: Access Paper: View a PDF of the paper titled On Hodge structures of compact complex manifolds with semistable degenerations, by Taro Sano View PDF HTML (experimental) TeX Source view license Current browse context: math.AG < prev | next > new | recent | 2024-05 Change to browse by: math References & Citations NASA ADS Google Scholar Semantic Scholar export BibTeX citation Loading... BibTeX formatted citation × loading... Data provided by: 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) Major funding support from

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