Polynome de Bernstein-Sato generique local

Details Polynome de Bernstein-Sato generique local Polynome de Bernstein-Sato generique local

2004-10-04

arxiv.org/abs/math/0410046v2

Mathematics

Algebraic Geometry

24 pages, in french. To appear in Journal of the Mathematical Society of Japan

Scientific paper

Given a family of analytic functions near 0 \in C^n parametrized by a smooth space, we study the Bernstein polynomial of the fiber on an irreducible variety V of the space of parameters and we show that it is generically constant. We prove that this polynomial b(s) satisfies a functional equation on V from which we derive a contructible stratification of the space of parameters by the Bernstein polynomial of the fiber. When the hypersurface admits generically a unique singularity at 0 \in C^n, we prove that b(s) is the generic Bernstein polynomial in the sense of Brian\c{c}on-Geandier-Maisonobe. The tools for the proofs are a formal generalization of an algorithm by Oaku and the generic standard bases studied by the author.

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