Bernstein-Sato Polynomials and Spectral Numbers

Guimarães, Andréa G.; Hefez, Abramo

Annales de l'Institut Fourier, Tome 57 (2007) no. 6, pp. 2031-2040.

Dans cet article nous décrivons un ensemble de racines du polynôme de Bernstein-Sato associées à un germe de fonction analytique à plusieurs variables complexes, avec un point critique isolé à l’origine, qui peuvent être obtenues en connaissant seulement les nombres spectraux du germe. Ceci nous donnera aussi un ensemble de racines communes aux polynômes de Bernstein-Sato associées aux membres d’une famille à $\mu$-constant de germes de fonctions. Un exemple nous montrera que cet ensemble peut parfois donner toutes les racines communes.

In this paper we will describe a set of roots of the Bernstein-Sato polynomial associated to a germ of complex analytic function in several variables, with an isolated critical point at the origin, that may be obtained by only knowing the spectral numbers of the germ. This will also give us a set of common roots of the Bernstein-Sato polynomials associated to the members of a $\mu$-constant family of germs of functions. An example will show that this set may sometimes consist of all common roots.

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