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

• Autorzy: M. Hickel
• Języki publikacji: FR EN

Abstrakty

EN

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.

Kategorie tematyczne

• 13J07: Analytical algebras and rings
• 13C10: Projective and free modules and ideals

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Annales Polonici Mathematici
• Rocznik: 2008
• Tom: 94
• Numer: 3
• Strony: 245-264

Daty

wydano

2008

Twórcy

autor

M. Hickel

• Équipe d'Analyse et Géométrie, Université Bordeaux 1, I.M.B.
• Département Informatique, I.U.T. Bordeaux 1, 33405 Talence Cedex, France

Identyfikatory

DOI

10.4064/ap94-3-4