Une note à propos du Jacobien de $n$ fonctions holomorphes à l'origine de $\mathbb{C}^n$
| dc.creator | Hickel, Michel | |
| dc.date | 2008-02-04 | |
| dc.date.accessioned | 2026-07-07T09:47:57Z | |
| dc.date.available | 2026-07-07T09:47:57Z | |
| dc.description | Let $f_1,...,f_n$ be $n$ germs of holomorphic functions at the origin of $\mathbb{C}^n$ such that $f_i(0)=0$, $1\leq i\leq n$. We give a proof based on the J. Lipman's theory of residues via Hochschild Homology that the Jacobian of $f_1,...,f_n$ belongs to the ideal generated by $f_1,...,f_n$ belongs to the ideal generated by $f_1,...,f_n$ if and only if the dimension ot the germ of common zeos of $f_1,...,f_n$ is sttrictly positive. In fact we prove much more general results which are relatives versions of this result replacing the field $\mathbb{C}$ by convenient noetherian rings $\mathbf{A}$ (c.f. Th. 3.1 and Th. 3.3). We then show a Łojasiewicz inequality for the jacobian analogous to the classical one by S. Łojasiewicz for the gradient. | |
| dc.identifier | https://arxiv.org/abs/0802.0426 | |
| dc.identifier | http://arxiv.org/abs/0802.0426 | |
| dc.identifier | Annales Polonici Mathematici (2008) 1-22 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/164032 | |
| dc.subject | Algebraic Geometry | |
| dc.title | Une note à propos du Jacobien de $n$ fonctions holomorphes à l'origine de $\mathbb{C}^n$ | |
| dc.type | text |