2004/10/04 by Rouchdi Bahloul, Bahloul, Rouchdi
Computer Science · Engineering · Mathematics · #Advanced Numerical Analysis Techniques #Algebraic Geometry (math.AG) #FOS: Mathematics #Polynomial and algebraic computation #math.AG
paper · pdf · doi:10.48550/arxiv.math/0410046
24 pages, in french. To appear in Journal of the Mathematical Society of Japan
openalex publication_date 2004/10/04 · arxiv created 2005/10/04 · arxiv updated 2016/09/07 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Given a family of analytic functions near 0 ∈ Cn 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 ∈ Cn, we prove that b(s) is the generic Bernstein polynomial in the sense of Briançon-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.