Permutation-equivariant quantum K-theory of Fermat singularities

[2410.17730] Permutation-equivariant quantum K-theory of Fermat singularities Skip to main content Search Submit Donate Log in Search arXiv Press Enter to search · Advanced search Mathematics > Algebraic Geometry arXiv:2410.17730 (math) [Submitted on 23 Oct 2024 ( v1 ), last revised 9 Apr 2026 (this version, v2)] Title: Permutation-equivariant quantum K-theory of Fermat singularities Authors: Maxime Cazaux View a PDF of the paper titled Permutation-equivariant quantum K-theory of Fermat singularities, by Maxime Cazaux View PDF HTML (experimental) Abstract: We compute the genus-0 permutation-equivariant quantum K-theory of Fermat singularities, in parallel with the Givental-Lee theory for projective varieties. We extend Givental-Tonita's formalism of adelic Lagrangian cones to the singularity theory, and we obtain explicit $I$-functions for the invariants, which satisfy the same $q$-difference equation as Givental's $I$-function of the associated hypersurface. This can be regarded as an extension of the Landau-Ginzburg/Calabi-Yau correspondence, although a discrepancy between the two sides sides emerges in K-theory. In the case of the quintic threefold, both generating functions satisfy a $q$-difference equation of degree $25$; the hypersurface $I$-function only spans a $5$-dimensional subspace of solutions, while the singularity $I$-function spans the full space of solutions. Subjects: Algebraic Geometry (math.AG) Cite as: arXiv:2410.17730 [math.AG] (or arXiv:2410.17730v2 [math.AG] for this version) https://doi.org/10.48550/arXiv.2410.17730 Focus to learn more arXiv-issued DOI via DataCite Submission history From: Maxime Cazaux [ view email ] [v1] Wed, 23 Oct 2024 10:01:44 UTC (36 KB) [v2] Thu, 9 Apr 2026 02:49:36 UTC (42 KB) Full-text links: Access Paper: View a PDF of the paper titled Permutation-equivariant quantum K-theory of Fermat singularities, by Maxime Cazaux View PDF HTML (experimental) TeX Source view license Current browse context: math.AG < prev | next > new | recent | 2024-10 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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