Une note à propos du Jacobien de $n$ fonctions holomorphes à l'origine de $\mathbb{C}^n$
| hal.structure.identifier | Institut de Mathématiques de Bordeaux [IMB] | |
| dc.contributor.author | HICKEL, Michel | |
| dc.date.accessioned | 2024-04-04T02:58:46Z | |
| dc.date.available | 2024-04-04T02:58:46Z | |
| dc.date.created | 2008-02-02 | |
| dc.date.issued | 2008 | |
| dc.identifier.issn | 0066-2216 | |
| dc.identifier.uri | https://oskar-bordeaux.fr/handle/20.500.12278/192684 | |
| dc.description.abstractEn | Let $f_1,\ldots,f_n$ 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 $f_1,\ldots,f_n$ belongs to the ideal generated by $f_1,\ldots,f_n$ belongs to the ideal generated by $f_1,\ldots,f_n$ if and only if the dimension ot the germ of common zeos of $f_1,\ldots,f_n$ 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 \L ojasiewicz inequality for the jacobian analogous to the classical one by S. \L ojasiewicz for the gradient. | |
| dc.language.iso | fr | |
| dc.publisher | Instytut Matematyczny Polskiej Akademii Nauk | |
| dc.title | Une note à propos du Jacobien de $n$ fonctions holomorphes à l'origine de $\mathbb{C}^n$ | |
| dc.type | Article de revue | |
| dc.subject.hal | Mathématiques [math]/Géométrie algébrique [math.AG] | |
| dc.identifier.arxiv | 0802.0426 | |
| bordeaux.journal | Annales Polonici Mathematici | |
| bordeaux.page | 245-264 | |
| bordeaux.volume | 94 | |
| bordeaux.hal.laboratories | Institut de Mathématiques de Bordeaux (IMB) - UMR 5251 | * |
| bordeaux.issue | 3 | |
| bordeaux.institution | Université de Bordeaux | |
| bordeaux.institution | Bordeaux INP | |
| bordeaux.institution | CNRS | |
| bordeaux.peerReviewed | oui | |
| hal.identifier | hal-00238383 | |
| hal.version | 1 | |
| hal.popular | non | |
| hal.audience | Internationale | |
| hal.origin.link | https://hal.archives-ouvertes.fr//hal-00238383v1 | |
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