Warianty tytułu
Języki publikacji
Abstrakty
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.
Słowa kluczowe
Kategorie tematyczne
Czasopismo
Rocznik
Tom
Numer
Strony
245-264
Opis fizyczny
Daty
wydano
2008
Twórcy
autor
- Équipe d'Analyse et Géométrie, Université Bordeaux 1, I.M.B.
- Département Informatique, I.U.T. Bordeaux 1, 33405 Talence Cedex, France
Bibliografia
Typ dokumentu
Bibliografia
Identyfikatory
DOI
Identyfikator YADDA
bwmeta1.element.bwnjournal-article-doi-10_4064-ap94-3-4