{"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/decomposing-jacobians-via-galois-covers","title":"Decomposing Jacobians via Galois covers","arxiv_id":"2003.07774","date":"2020-03-17","proceeding":null,"authors":["Davide Lombardo","Elisa Lorenzo García","Christophe Ritzenthaler","Jeroen Sijsling"],"abstract":"Let $\\phi:\\,X\\rightarrow Y$ be a (possibly ramified) cover between two algebraic curves of positive genus. We develop tools that may identify the Prym variety of $\\phi$, up to isogeny, as the Jacobian of a quotient curve $C$ in the Galois closure of the composition of $\\phi$ with a well-chosen map $Y\\rightarrow \\mathbb{P}^1$. This method allows us to recover all previously obtained descriptions of a Prym variety in terms of a Jacobian that are known to us, besides yielding new applications. We also find algebraic equations for some of these new cases, including one where $X$ has genus $3$, $Y$ has genus $1$ and $\\phi$ is a degree $3$ map totally ramified over $2$ points.","url_abs":"http://arxiv.org/abs/2003.07774v1","url_pdf":"http://arxiv.org/pdf/2003.07774v1.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":"decomposing-jacobians-via-galois-covers","repo_url":"https://github.com/JRSijsling/prym_decomposition","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":0,"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}