163306 20251024172259.0 doi 10.4064/ap240920-4-4 sideral 145721 ART-2025-145721 eng Artal Bartolo, Enrique Universidad de Zaragoza (orcid)0000-0002-8276-5116 Milnor number of plane curve singularities in arbitrary characteristic 2025 Reduced power series in two variables with coefficients in a field of characteristic zero satisfy a well-known formula that relates a codimension related to the normalization of a ring and the Jacobian ideal. In the general case Deligne proved that this formula is only an inequality; García Barroso and Płoski stated a conjecture for irreducible power series. In this work we generalize Kouchnirenko’s formula for any reduced power series and also generalize García Barroso and Płoski’s conjecture. We prove the conjecture in some cases using in particular Greuel–Nguyen’s results. Access copy available to the general public Unrestricted info:eu-repo/grantAgreement/ES/DGA/E22-20R info:eu-repo/grantAgreement/ES/MICINN/PID2020-114750GB-C31/AEI/10.13039/501100011033 info:eu-repo/grantAgreement/ES/MICINN/PID2020-114750GB-C32/AEI/10.13039/501100011033 info:eu-repo/semantics/openAccess by https://creativecommons.org/licenses/by/4.0/deed.es info:eu-repo/semantics/article info:eu-repo/semantics/publishedVersion Cassou-Noguès, Pierrette 2006 440 Universidad de Zaragoza Dpto. Matemáticas Área Geometría y Topología (2025), [23 pp.] Annales Polonici Mathematici Annales Polonici Mathematici 0066-2216 581741 http://zaguan.unizar.es/record/163306/files/texto_completo.pdf Versión publicada 1113622 http://zaguan.unizar.es/record/163306/files/texto_completo.jpg?subformat=icon icon Versión publicada oai:zaguan.unizar.es:163306 articulos driver 2025-10-24-16:56:50 ARTICLE