2003/11/26 by Rouchdi Bahloul, Bahloul, Rouchdi
Engineering · Mathematics · Physics and Astronomy · #16S32 #32C38 #Advanced Differential Geometry Research #Advanced Numerical Analysis Techniques #Advanced Topics in Algebra #Complex Variables (math.CV) #FOS: Mathematics #Rings and Algebras (math.RA) #math.CV #math.RA #msc:16S32 #msc:32C38
paper · pdf · doi:10.48550/arxiv.math/0311463
in french, 17 pages, no figures. Accepted version in Kyushu J. Math
openalex publication_date 2003/11/26 · arxiv created 2005/03/18 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Let f1 and f2 be two semi-universal deformations of quasi homogeneous polynomials in two variables respectively for the weight vectors ρ1 and ρ2 such that they satisfy similar conditions to that of semi quasi homogeneous singularities for one weight. By methods inspired by H. Maynadier's, we give an explicit formula for a Bernstein-Sato polynomial involving two affine forms ρi(f1) s1 + ρi(f2) s2 +k, i=1,2. In the particular case (f1, f2)=(x1a+x2b, x1c+x2d), we calculate the space Hf recently studied by J. Briançon, Ph. Maisonobe and M. Merle and we show that it is equal to the zero set of s1 s2 (ab s1+ ad s2)(ad s1+ cd s2).