A Lê-Greuel type formula for the image Milnor number
Let $f\colon (\mathbb{C}^n,0)\to (\mathbb{C}^{n+1},0)$ be a corank 1 finitely determined map germ. For a generic linear form $p\colon (\mathbb{C}^{n+1},0)\to(\mathbb{C},0)$ we denote by $g\colon (\mathbb{C}^{n-1},0)\to (\mathbb{C}^{n},0)$ the transverse slice of $f$ with respect to $p$. We prove tha...
| Autores: | , |
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| Tipo de recurso: | artículo |
| Estado: | Versión publicada |
| Fecha de publicación: | 2019 |
| País: | España |
| Institución: | Basque Center for Applied Mathematics (BCAM) |
| Repositorio: | BIRD. BCAM's Institutional Repository Data |
| OAI Identifier: | oai:bird.bcamath.org:20.500.11824/992 |
| Acceso en línea: | http://hdl.handle.net/20.500.11824/992 |
| Access Level: | acceso embargado |
| Palabra clave: | Image Milnor number Lê-Greuel formula Finite determinacy |
| Sumario: | Let $f\colon (\mathbb{C}^n,0)\to (\mathbb{C}^{n+1},0)$ be a corank 1 finitely determined map germ. For a generic linear form $p\colon (\mathbb{C}^{n+1},0)\to(\mathbb{C},0)$ we denote by $g\colon (\mathbb{C}^{n-1},0)\to (\mathbb{C}^{n},0)$ the transverse slice of $f$ with respect to $p$. We prove that the sum of the image Milnor numbers $\mu_I(f)+\mu_I(g)$ is equal to the number of critical points of $p|_{X_s}\colon X_s\to\mathbb{C}$ on all the strata of $X_s$, where $X_s$ is the disentanglement of $f$ (i.e., the image of a stabilisation $f_s$ of $f$). |
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