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...
| Autores: | , , |
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| 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 |
| 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. |
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