{"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/families-of-pairs-of-genus-2-curves-with","title":"Families of Pairs of Genus 2 Curves with Isomorphic Unpolarized Jacobians","arxiv_id":"2410.03664","date":"2024-10-04","proceeding":null,"authors":["Raghda Abdellatif"],"abstract":"We construct three families of pairs of genus 2 curves over a field K, whose Jacobians are isomorphic as unpolarized abelian varieties. Each family is parameterized by an open subset of the Projective line over K. Our construction is based on a remark in a paper by Howe. Later, we describe an obstruction to perusing the same technique over Q.","url_abs":"https://arxiv.org/abs/2410.03664v1","url_pdf":"https://arxiv.org/pdf/2410.03664v1.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":"families-of-pairs-of-genus-2-curves-with","repo_url":"https://github.com/RaghdaAbdellatif/Pairs-Isomorphic-Jacobians","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}