{"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/multiplier-ideals-of-plane-curve","title":"Multiplier ideals of plane curve singularities via Newton polygons","arxiv_id":"2109.13294","date":"2021-09-27","proceeding":null,"authors":["Pedro D. González Pérez","Manuel González Villa","Carlos R. Guzmán Durán","Miguel Robredo Buces"],"abstract":"We give an effective method to determine the multiplier ideals and jumping numbers associated with a curve singularity $C$ in a smooth surface. We characterize the multiplier ideals in terms of certain Newton polygons, generalizing a theorem of Howald, which holds when $C$ is Newton non-degenerate with respect to some local coordinate system. The method uses toroidal embedded resolutions and generating sequences of families of valuations, and can be extended to some classes of higher dimensional hypersurface singularities.","url_abs":"https://arxiv.org/abs/2109.13294v2","url_pdf":"https://arxiv.org/pdf/2109.13294v2.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":"multiplier-ideals-of-plane-curve","repo_url":"https://github.com/tdimitch/jumping-numbers","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}