On the affine invariant of simple hypersemitoric systems

[2411.17509] On the affine invariant of simple hypersemitoric systems Skip to main content Search Submit Donate Log in Search arXiv Press Enter to search · Advanced search Mathematics > Symplectic Geometry arXiv:2411.17509 (math) [Submitted on 26 Nov 2024 ( v1 ), last revised 10 Apr 2026 (this version, v2)] Title: On the affine invariant of simple hypersemitoric systems Authors: Konstantinos Efstathiou , Sonja Hohloch , Pedro Santos View a PDF of the paper titled On the affine invariant of simple hypersemitoric systems, by Konstantinos Efstathiou and 2 other authors View PDF HTML (experimental) Abstract: Hypersemitoric systems are a class of integrable systems on $4$-dimensional symplectic manifolds which only have mildly degenerate singularities and where one of the integrals induces an effective Hamiltonian $S^1$-action and is proper. We introduce the affine invariant of hypersemitoric systems, which is a generalization of the Delzant polytope of toric systems and the polytope invariant of semitoric systems. Along the way, we compute and plot this invariant for meaningful and more and more complicated examples. Comments: 76 pages, 28 figures Subjects: Symplectic Geometry (math.SG) ; Dynamical Systems (math.DS); Exactly Solvable and Integrable Systems (nlin.SI) MSC classes: 53D05, 53D20, 37J35, 70H06 Cite as: arXiv:2411.17509 [math.SG] (or arXiv:2411.17509v2 [math.SG] for this version) https://doi.org/10.48550/arXiv.2411.17509 Focus to learn more arXiv-issued DOI via DataCite Submission history From: Pedro Santos [ view email ] [v1] Tue, 26 Nov 2024 15:18:58 UTC (19,951 KB) [v2] Fri, 10 Apr 2026 12:52:06 UTC (20,016 KB) Full-text links: Access Paper: View a PDF of the paper titled On the affine invariant of simple hypersemitoric systems, by Konstantinos Efstathiou and 2 other authors View PDF HTML (experimental) TeX Source view license Current browse context: math.SG < prev | next > new | recent | 2024-11 Change to browse by: math math.DS nlin nlin.SI 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

• Minuscule Relations in Quantum $K$-Theory of Flag Varieties#1035766
• Reducibility of symmetry on $q$-Painlevé equations#925310
• Reducibility of symmetry on $q$-Painlevé equations#921074
• Notions of Anosov representation of relatively hyperbolic groups#149147
• AF-action groupoid models for diagonal AH-algebras#609644