{"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/equations-of-riemann-surfaces-with","title":"Equations of Riemann surfaces with automorphisms","arxiv_id":"1607.04778","date":"2016-07-16","proceeding":null,"authors":["David Swinarski"],"abstract":"We present an algorithm for computing equations of canonically embedded Riemann surfaces with automorphisms. A variant of this algorithm with many heuristic improvements is used to produce equations of Riemann surfaces $X$ with large automorphism groups (that is, $|\\mathrm{Aut}(X)| > 4(g_X-1)$) for genus $4 \\leq g_X \\leq 7$. The main tools are the Eichler trace formula for the character of the action of $\\mathrm{Aut}(X)$ on holomorphic differentials, algorithms for producing matrix generators of a representation of a finite group with a specified irreducible character, and Gr\\\"obner basis techniques for computing flattening stratifications.","url_abs":"http://arxiv.org/abs/1607.04778v1","url_pdf":"http://arxiv.org/pdf/1607.04778v1.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":"equations-of-riemann-surfaces-with","repo_url":"https://github.com/jenpaulhus/group-actions-RS","is_official":0,"mentioned_in_paper":0,"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}