{"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/some-evidence-for-the-coleman-oort-conjecture","title":"Some evidence for the Coleman-Oort conjecture","arxiv_id":"2102.12349","date":"2021-02-24","proceeding":null,"authors":["Diego Conti","Alessandro Ghigi","Roberto Pignatelli"],"abstract":"The Coleman-Oort conjecture says that for large $g$ there are no positive-dimensional Shimura subvarieties of $\\mathsf{A}_g$ generically contained in the Jacobian locus. Counterexamples are known for $g\\leq 7$. They can all be constructed using families of Galois coverings of curves satisfying a numerical condition. These families are already classified in cases where: a) the Galois group is cyclic, b) it is abelian and the family is 1-dimensional, and c) $g\\leq 9$. By means of carefully designed computations and theoretical arguments excluding a large number of cases we are able to prove that for $g\\leq 100$ there are no other families than those already known.","url_abs":"https://arxiv.org/abs/2102.12349v2","url_pdf":"https://arxiv.org/pdf/2102.12349v2.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":"some-evidence-for-the-coleman-oort-conjecture","repo_url":"https://github.com/diego-conti/centone","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":1,"framework":"none","reach":null},{"paper_slug":"some-evidence-for-the-coleman-oort-conjecture","repo_url":"https://github.com/diego-conti/gullinbursti","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}