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

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Hickel M.

Annales Polonici Mathematici

2008

tom 94

nr 3

245-264

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.

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1 Annales Polonici Mathematici

1 Hickel M.

1 2008

Wyniki wyszukiwania

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