Une note à propos du jacobien de n fonctions holomorphes à l'origine de ℂⁿ

M. Hickel

Annales Polonici Mathematici (2008)

  • Volume: 94, Issue: 3, page 245-264
  • ISSN: 0066-2216

Abstract

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Let f₁,...,fₙ be n germs of holomorphic functions at the origin of ℂⁿ, such that f i ( 0 ) = 0 , 1 ≤ i ≤ n. We give a proof based on J. Lipman’s theory of residues via Hochschild homology that the jacobian of f₁,...,fₙ belongs to the ideal generated by f₁,...,fₙ if and only if the dimension of the germ of common zeros of f₁,...,fₙ is strictly positive. In fact, we prove much more general results which are relative versions of this result replacing the field ℂ by convenient noetherian rings A (Ths. 3.1 and 3.3). We then show a Łojasiewicz inequality for the jacobian analogous to the classical one by S. Łojasiewicz for the gradient.

How to cite

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M. Hickel. "Une note à propos du jacobien de n fonctions holomorphes à l'origine de ℂⁿ." Annales Polonici Mathematici 94.3 (2008): 245-264. <http://eudml.org/doc/280524>.

@article{M2008,
author = {M. Hickel},
journal = {Annales Polonici Mathematici},
language = {fre},
number = {3},
pages = {245-264},
title = {Une note à propos du jacobien de n fonctions holomorphes à l'origine de ℂⁿ},
url = {http://eudml.org/doc/280524},
volume = {94},
year = {2008},
}

TY - JOUR
AU - M. Hickel
TI - Une note à propos du jacobien de n fonctions holomorphes à l'origine de ℂⁿ
JO - Annales Polonici Mathematici
PY - 2008
VL - 94
IS - 3
SP - 245
EP - 264
LA - fre
UR - http://eudml.org/doc/280524
ER -

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