{"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/chow-rings-of-low-degree-hurwitz-spaces","title":"Chow rings of low-degree Hurwitz spaces","arxiv_id":"2110.01059","date":"2021-10-03","proceeding":null,"authors":["Samir Canning","Hannah Larson"],"abstract":"While there is much work and many conjectures surrounding the intersection theory of the moduli space of curves, relatively little is known about the intersection theory of the Hurwitz space $\\mathcal{H}_{k, g}$ parametrizing smooth degree $k$, genus $g$ covers of $\\mathbb{P}^1$. Let $k = 3, 4, 5$. We prove that the rational Chow rings of $\\mathcal{H}_{k,g}$ stabilize in a suitable sense as $g$ tends to infinity. In the case $k = 3$, we completely determine the Chow rings for all $g$. We also prove that the rational Chow groups of the simply branched Hurwitz space $\\mathcal{H}^s_{k,g} \\subset \\mathcal{H}_{k,g}$ are zero in codimension up to roughly $g/k$. In subsequent work, results developed in this paper are used to prove that the Chow rings of $\\mathcal{M}_7, \\mathcal{M}_8,$ and $\\mathcal{M}_9$ are tautological.","url_abs":"https://arxiv.org/abs/2110.01059v1","url_pdf":"https://arxiv.org/pdf/2110.01059v1.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":"chow-rings-of-low-degree-hurwitz-spaces","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}