Non-proportional wall crossing for K-stability

[2412.15725] Non-proportional wall crossing for K-stability Skip to main content Search Submit Donate Log in Search arXiv Press Enter to search · Advanced search Mathematics > Algebraic Geometry arXiv:2412.15725 (math) [Submitted on 20 Dec 2024 ( v1 ), last revised 20 Mar 2026 (this version, v2)] Title: Non-proportional wall crossing for K-stability Authors: Yuchen Liu , Chuyu Zhou View a PDF of the paper titled Non-proportional wall crossing for K-stability, by Yuchen Liu and Chuyu Zhou View PDF HTML (experimental) Abstract: In this paper, we present a general wall crossing theory for K-stability and K-moduli of log Fano pairs whose boundary divisors can be non-proportional to the anti-canonical divisor. Along the way, we prove that there are only finitely many K-semistable domains associated to the fibers of a log bounded family of couples. Under the additional assumption of volume bounded from below, we show that K-semistable domains are semi-algebraic sets (although not necessarily polytopes). As a consequence, we obtain a finite semi-algebraic chamber decomposition for wall crossing of K-moduli spaces. In the case of one boundary divisor, this decomposition is an expected finite interval chamber decomposition. As an application of the theory, we prove a comparison theorem between GIT-stability and K-stability in non-proportional setting when the coefficient of the boundary is sufficiently small. Comments: Accepted version by Proc. London Math. Soc., 62 pages, comments welcome Subjects: Algebraic Geometry (math.AG) Cite as: arXiv:2412.15725 [math.AG] (or arXiv:2412.15725v2 [math.AG] for this version) https://doi.org/10.48550/arXiv.2412.15725 Focus to learn more arXiv-issued DOI via DataCite Journal reference: Proc. London Math. Soc. (2026) Volume 132, Issue 4, e70157 Submission history From: Chuyu Zhou [ view email ] [v1] Fri, 20 Dec 2024 09:48:26 UTC (85 KB) [v2] Fri, 20 Mar 2026 07:50:45 UTC (87 KB) Full-text links: Access Paper: View a PDF of the paper titled Non-proportional wall crossing for K-stability, by Yuchen Liu and Chuyu Zhou 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

Related documents

• Multidisciplinary System Design Optimization#3595
• Finding the K best synthesis plans#632959
• Le design pour le réemploi des matériaux de construction : une recherche-projet sur le cas des plafonds démontables#161163
• Maximizing Algebraic Connectivity with $2(n-2)$ Edges: The Large Vertex Number Case#1084316
• Subsystem localization in a two-leg ladder system#635593