Local invariants on quotient singularities and a genus formula for weighted plane curves

Cogolludo-Agustín, J. I. (Universidad de Zaragoza) ; Martín-Morales, J. ; Ortigas-Galindo, J.

Resumen: In this paper, we extend the concept of Milnor fiber and Milnor number to curve germs on surface quotient singularities. A generalization of the local d-invariant is defined and described in terms of a Q-resolution of the curve singularity. In particular, when applied to the classical case (the ambient space is a smooth surface) one obtains a formula for the classical d-invariant in terms of a Q-resolution, which simplifies considerably effective computations. All these tools will finally allow for an explicit description of the genus formula of a curve defined on a weighted projective plane in terms of its degree and the local type of its singularities.

Idioma: Inglés

DOI: 10.1093/imrn/rnt052

Año: 2014

Publicado en: INTERNATIONAL MATHEMATICS RESEARCH NOTICES 2014, 13 (2014), 3559-3581
ISSN: 1073-7928

Factor impacto JCR: 1.1 (2014)

Categ. JCR: MATHEMATICS rank: 42 / 310 = 0.135 (2014) - Q1 - T1

Financiación: info:eu-repo/grantAgreement/ES/DGA/E15
Financiación: info:eu-repo/grantAgreement/ES/MICINN/MTM2010-21740-C02-02

Tipo y forma: Artículo (PostPrint)

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