{"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/classical-limit-of-genus-two-daha","title":"Classical Limit of genus two DAHA","arxiv_id":"2309.01011","date":"2023-09-02","proceeding":null,"authors":["S. Arthamonov"],"abstract":"We show that one-parameter deformation $\\mathcal A_{q,t}$ of the skein algebra $Sk_q(\\Sigma_2)$ of a genus two surface suggested in [AS19] is flat. We solve the word problem in the algebra and describe monomial basis. In addition, we calculate the classical limit $\\mathcal A_{q=1,t}$ of the algebra and prove that it is a one-parameter flat Poisson deformation of the coordinate ring $\\mathcal A_{q=t=1}$ of an $SL(2,\\mathbb C)$-charater variety of a genus two surface. As a byproduct, we obtain a remarkably simple presentation in terms of generators and relations for the coordinate ring $\\mathcal A_{q=t=1}$ of a genus two character variety.","url_abs":"https://arxiv.org/abs/2309.01011v2","url_pdf":"https://arxiv.org/pdf/2309.01011v2.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":"classical-limit-of-genus-two-daha","repo_url":"https://github.com/semeonart/genustwodaha-basis","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":1,"framework":"none","reach":null}],"tasks":[],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"syntology_url":null,"atlas_url":null,"mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}