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Polynômes de Bernstein et déformations à nombre de Milnor constant. (Bernstein polynomials and deformations preserving Milnor’s number). (French) Zbl 0696.32010
Let F(x,\b{y})\(=0\) be the equation of a germ of deformation with respect to a parameter \b{y} of an isolated singularity of a hypersurface of \({\mathbb{C}}^ n\). One defines the notion of a good operator in s and one proves the existence of a Bernstein polynomial of the generic fibre of the deformation (Theorem 1). Then, if the deformation preserves Milnor’s number, the author proves the existence of a relative Bernstein-Sato polynomial of F (Theorem 2). Finally, one gives a relative version of a result of Kashiwara: If F preserves Milnor’s number, then there exists a good operator in s annihilating \(F^ s\).

32S30 Deformations of complex singularities; vanishing cycles
32S05 Local complex singularities