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

Bahloul, Rouchdi

J. Math. Soc. Japan 58, No. 2, 595-616 (2006).

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.

Reviewer: Corina Baciu (Mainz)

MSC:

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