Local generic Bernstein-Sato polynomial. (Polynôme de Bernstein-Sato générique local.) (French) Zbl 1102.32015

In the present paper the author studies the Bernstein-Sato polynomial of the fiber over an irreducible variety of the parameter-space of a family of analytic functions. He shows that this polynomial is generically constant and derives a constructible stratification of the space of parameters by the Bernstein polynomial of the fibre. He uses the technique of generical standard bases and a generalization of an algorithm of Oaku that computes locally the Bernstein-Sato polynomial.


32S30 Deformations of complex singularities; vanishing cycles
16S32 Rings of differential operators (associative algebraic aspects)
13P99 Computational aspects and applications of commutative rings
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