Milnor number of plane curve singularities in arbitrary characteristic

Artal Bartolo, Enrique (Universidad de Zaragoza) ; Cassou-Noguès, Pierrette

Resumen: 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.

Idioma: Inglés

DOI: 10.4064/ap240920-4-4

Año: 2025

Publicado en: Annales Polonici Mathematici (2025), [23 pp.]
ISSN: 0066-2216

Financiación: info:eu-repo/grantAgreement/ES/DGA/E22-20R
Financiación: info:eu-repo/grantAgreement/ES/MICINN/PID2020-114750GB-C31/AEI/10.13039/501100011033
Financiación: info:eu-repo/grantAgreement/ES/MICINN/PID2020-114750GB-C32/AEI/10.13039/501100011033

Tipo y forma: Artículo (Versión definitiva)

Área (Departamento): Área Geometría y Topología (Dpto. Matemáticas)