Bruce-Roberts numbers and quasihomogeneous functions on analytic varieties

[EN] Given a germ of an analytic variety X and a germ of a holomorphic function f with a stratified isolated singularity with respect to the logarithmic stratification of X, we show that under certain conditions on the singularity type of the pair (f,X), the following relative analog of the well-kno...

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Detalles Bibliográficos
Autores: Bivià-Ausina, Carles|||0000-0003-0784-3353, Kourliouros, Konstantinos, Ruas, M. A. S.
Tipo de recurso: artículo
Fecha de publicación:2024
País:España
Institución:Universitat Politècnica de València (UPV)
Repositorio:RiuNet. Repositorio Institucional de la Universitat Politécnica de Valéncia
Idioma:inglés
OAI Identifier:oai:riunet.upv.es:10251/222862
Acceso en línea:https://riunet.upv.es/handle/10251/222862
Access Level:acceso abierto
Palabra clave:Bruce-Roberts numbers
Quasihomogeneous functions
Analytic varieties
Logarithmic vector fields
Logarithmic stratification
Stratified isolated singularities
Descripción
Sumario:[EN] Given a germ of an analytic variety X and a germ of a holomorphic function f with a stratified isolated singularity with respect to the logarithmic stratification of X, we show that under certain conditions on the singularity type of the pair (f,X), the following relative analog of the well-known K. Saito¿s theorem holds true: equality of the relative Milnor and Tjurina numbers of f with respect to X (also known as Bruce¿Roberts numbers) is equivalent to the relative quasihomogeneity of the pair (f, X), i.e. to the existence of a coordinate system such that both f and X are quasihomogeneous with respect to the same positive rational weights.