{"about":{"site":"https://codewithpapers.app","non_affiliation":"Code with Papers and Syntology are not affiliated with, endorsed by, or sponsored by Papers with Code, Meta, or the pwc-archive mirror.","licence":"CC BY-SA 4.0","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","attribution":"https://codewithpapers.app/attribution","modified":"archive material modified by Syntology; see the attribution page"},"url":"/paper/arithmetic-and-thin-monodromy-in-mathrm-sp-6","title":"Thin monodromy in $\\mathrm{Sp}(4)$ and $\\mathrm{Sp}(6)$","arxiv_id":"2112.12111","date":"2021-12-22","proceeding":null,"authors":["Jitendra Bajpai","Daniele Dona","Martin Nitsche"],"abstract":"We explore the thinness of hypergeometric groups of type $\\mathrm{Sp}(4)$ and $\\mathrm{Sp}(6)$ by applying a new approach of computer-assisted ping pong. We prove the thinness of $17$ hypergeometric groups with maximally unipotent monodromy in $\\mathrm{Sp}(6)$, completing the classification of all $40$ such groups into arithmetic and thin cases. In addition, we establish the thinness of further $46$ hypergeometric groups in $\\mathrm{Sp}(6)$, and of $3$ hypergeometric groups in $\\mathrm{Sp}(4)$, completing the classification of all $\\mathrm{Sp}(4)$ hypergeometric groups. To the best of our knowledge, this article produces the first $63$ examples in the cyclotomic family of Zariski dense non-arithmetic hypergeometric monodromy groups of real rank three.","url_abs":"https://arxiv.org/abs/2112.12111v3","url_pdf":"https://arxiv.org/pdf/2112.12111v3.pdf","source":{"archive":"pwc-archive (Hugging Face), CC BY-SA 4.0","snapshot":"2025-07-28","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","row_kind":"links_only","authors_date_abstract":"arXiv metadata, CC0 1.0 (https://info.arxiv.org/help/license), from the Kaggle arXiv metadata snapshot of 2026-09-12"},"code_links":[{"paper_slug":"arithmetic-and-thin-monodromy-in-mathrm-sp-6","repo_url":"https://github.com/daniele-dona/sage-bdn21","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":0,"framework":"none","reach":null}],"tasks":[],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":null,"mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}