On the coupled stability thresholds of graded linear series

[2412.04019] On the coupled stability thresholds of graded linear series Skip to main content Search Submit Donate Log in Search arXiv Press Enter to search · Advanced search Mathematics > Algebraic Geometry arXiv:2412.04019 (math) [Submitted on 5 Dec 2024 ( v1 ), last revised 9 Apr 2026 (this version, v2)] Title: On the coupled stability thresholds of graded linear series Authors: Kento Fujita View a PDF of the paper titled On the coupled stability thresholds of graded linear series, by Kento Fujita View PDF HTML (experimental) Abstract: In this paper, we see several basic properties of graded linear series. We firstly see that, if a graded linear series contains an ample series, then so are the pullbacks of the system under birational morphisms. Using this proposition, we define the refinements of graded linear series with respects to primitive flags. Moreover, we give several formulas to compute the $S$-invariant of those refinements. Secondly, we introduce the notion of coupled stability thresholds for graded linear series, which is a generalization of the notion introduced by Rubinstein--Tian--Zhang. We see that, over the interior of the support for finite numbers of graded linear series containing an ample series, the coupled stability threshold function can be uniquely extended continuously, which generalizes the work by Kewei Zhang. Thirdly, we get a product-type formula for coupled stability thresholds, which generalizes the work of Zhuang. Fourthly, we see Abban--Zhuang's type formulas for estimating local coupled stability thresholds. Comments: 74 pages; accepted by Journal of Mathematical Sciences, the University of Tokyo Subjects: Algebraic Geometry (math.AG) MSC classes: 14J45, 14L24 Cite as: arXiv:2412.04019 [math.AG] (or arXiv:2412.04019v2 [math.AG] for this version) https://doi.org/10.48550/arXiv.2412.04019 Focus to learn more arXiv-issued DOI via DataCite Submission history From: Kento Fujita [ view email ] [v1] Thu, 5 Dec 2024 09:56:20 UTC (59 KB) [v2] Thu, 9 Apr 2026 11:26:43 UTC (61 KB) Full-text links: Access Paper: View a PDF of the paper titled On the coupled stability thresholds of graded linear series, by Kento Fujita View PDF HTML (experimental) TeX Source view license Current browse context: math.AG < prev | next > new | recent | 2024-12 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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