000163306 001__ 163306 000163306 005__ 20251024172259.0 000163306 0247_ $$2doi$$a10.4064/ap240920-4-4 000163306 0248_ $$2sideral$$a145721 000163306 037__ $$aART-2025-145721 000163306 041__ $$aeng 000163306 100__ $$0(orcid)0000-0002-8276-5116$$aArtal Bartolo, Enrique$$uUniversidad de Zaragoza 000163306 245__ $$aMilnor number of plane curve singularities in arbitrary characteristic 000163306 260__ $$c2025 000163306 5060_ $$aAccess copy available to the general public$$fUnrestricted 000163306 5203_ $$aReduced 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. 000163306 536__ $$9info:eu-repo/grantAgreement/ES/DGA/E22-20R$$9info:eu-repo/grantAgreement/ES/MICINN/PID2020-114750GB-C31/AEI/10.13039/501100011033$$9info:eu-repo/grantAgreement/ES/MICINN/PID2020-114750GB-C32/AEI/10.13039/501100011033 000163306 540__ $$9info:eu-repo/semantics/openAccess$$aby$$uhttps://creativecommons.org/licenses/by/4.0/deed.es 000163306 655_4 $$ainfo:eu-repo/semantics/article$$vinfo:eu-repo/semantics/publishedVersion 000163306 700__ $$aCassou-Noguès, Pierrette 000163306 7102_ $$12006$$2440$$aUniversidad de Zaragoza$$bDpto. Matemáticas$$cÁrea Geometría y Topología 000163306 773__ $$g(2025), [23 pp.]$$pAnnales Polonici Mathematici$$tAnnales Polonici Mathematici$$x0066-2216 000163306 8564_ $$s581741$$uhttps://zaguan.unizar.es/record/163306/files/texto_completo.pdf$$yVersión publicada 000163306 8564_ $$s1113622$$uhttps://zaguan.unizar.es/record/163306/files/texto_completo.jpg?subformat=icon$$xicon$$yVersión publicada 000163306 909CO $$ooai:zaguan.unizar.es:163306$$particulos$$pdriver 000163306 951__ $$a2025-10-24-16:56:50 000163306 980__ $$aARTICLE