{"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/intersection-theory-on-low-degree-hurwitz","title":"Tautological classes on low-degree Hurwitz spaces","arxiv_id":"2103.09902","date":"2021-03-17","proceeding":null,"authors":["Samir Canning","Hannah Larson"],"abstract":"Let $\\mathcal{H}_{k,g}$ be the Hurwitz stack parametrizing degree $k$, genus $g$ covers of $\\mathbb{P}^1$. We define the tautological ring of $\\mathcal{H}_{k,g}$ and we show that all Chow classes, except possibly those supported on the locus of \"factoring covers,\" are tautological up to codimension roughly $g/k$ when $k \\leq 5$. The set-up developed here is also used in our subsequent work, wherein we prove new results about the structure of the Chow ring for $k \\leq 5$.","url_abs":"https://arxiv.org/abs/2103.09902v2","url_pdf":"https://arxiv.org/pdf/2103.09902v2.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":"intersection-theory-on-low-degree-hurwitz","repo_url":"https://github.com/src2165/Low-Degree-Hurwitz","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}