{"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/on-quartics-with-the-maximal-number-of-the","title":"On quartics with the maximal number of the maximal tangency lines","arxiv_id":"2410.13997","date":"2024-10-17","proceeding":null,"authors":["Łukasz Merta","Marcin Zieliński"],"abstract":"In this note, we examine the arrangements of lines and configurations of points that emerge from Fermat (von Dyck) and Komiya-Kuribayashi quartics. These quartics are characterized by having the maximum number of lines of maximal tangency, that is, lines for which the intersection multiplicity at the tangency point is equal to the degree of the curve. Additionally, we delve into the study of sextactic points on these quartics - points at which there exists a conic with the curve having a local intersection multiplicity of at least 6, which is one more than that observed at a general point - alongside the related configurations of conics.","url_abs":"https://arxiv.org/abs/2410.13997v1","url_pdf":"https://arxiv.org/pdf/2410.13997v1.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":"on-quartics-with-the-maximal-number-of-the","repo_url":"https://github.com/lukaszm111/singular-code---quartics","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}