{"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/torsion-divisors-of-plane-curves-and-zariski","title":"Torsion divisors of plane curves and Zariski pairs","arxiv_id":"1910.06490","date":"2019-10-15","proceeding":null,"authors":["E. Artal Bartolo","S. Bannai","T. Shirane","H. Tokunaga"],"abstract":"In this paper we study the embedded topology of reducible plane curves having a smooth irreducible component. In previous studies, the relation between the topology and certain torsion classes in the Picard group of degree zero of the smooth component was implicitly considered. We formulate this relation clearly and give a criterion for distinguishing the embedded topology in terms of torsion classes. Furthermore, we give a method of systematically constructing examples of curves where our criterion is applicable, and give new examples of Zariski tuples.","url_abs":"https://arxiv.org/abs/1910.06490v4","url_pdf":"https://arxiv.org/pdf/1910.06490v4.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":"torsion-divisors-of-plane-curves-and-zariski","repo_url":"https://github.com/enriqueartal/TorsionDivisorsZariskiPairs","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}