We discuss Bernstein polynomials of reductive linear free divisors. We define suitable Brieskorn lattices for these non-isolated singularities, and show the analogue of Malgrange’s result relating the roots of the Bernstein polynomial to the residue eigenvalues on the saturation of these Brieskorn lattices.
Dans ce travail, nous nous intéressons aux polynômes de Bernstein d’un diviseur linéairement libre réductif. Nous définissons un réseau de Brieskorn pour ces fonctions, qui sont des exemples de singularités non-isolées. Nous démontrons un théorème analogue au résultat de Malgrange qui relate les racines du polynôme de Bernstein aux valeurs propres du résidu de la saturation de ce réseau de Brieskorn.
Keywords: Brieskorn lattice, Bernstein polynomial, linear free divisors, spectral numbers
Mot clés : réseau de Brieskorn, polynôme de Bernstein, diviseur linéairement libre, nombres spectraux
@article{AIF_2011__61_1_379_0, author = {Sevenheck, Christian}, title = {Bernstein polynomials and spectral numbers for linear free divisors}, journal = {Annales de l'Institut Fourier}, pages = {379--400}, publisher = {Association des Annales de l{\textquoteright}institut Fourier}, volume = {61}, number = {1}, year = {2011}, doi = {10.5802/aif.2606}, zbl = {1221.34237}, mrnumber = {2828135}, language = {en}, url = {http://www.numdam.org/articles/10.5802/aif.2606/} }
TY - JOUR AU - Sevenheck, Christian TI - Bernstein polynomials and spectral numbers for linear free divisors JO - Annales de l'Institut Fourier PY - 2011 SP - 379 EP - 400 VL - 61 IS - 1 PB - Association des Annales de l’institut Fourier UR - http://www.numdam.org/articles/10.5802/aif.2606/ DO - 10.5802/aif.2606 LA - en ID - AIF_2011__61_1_379_0 ER -
%0 Journal Article %A Sevenheck, Christian %T Bernstein polynomials and spectral numbers for linear free divisors %J Annales de l'Institut Fourier %D 2011 %P 379-400 %V 61 %N 1 %I Association des Annales de l’institut Fourier %U http://www.numdam.org/articles/10.5802/aif.2606/ %R 10.5802/aif.2606 %G en %F AIF_2011__61_1_379_0
Sevenheck, Christian. Bernstein polynomials and spectral numbers for linear free divisors. Annales de l'Institut Fourier, Volume 61 (2011) no. 1, pp. 379-400. doi : 10.5802/aif.2606. http://www.numdam.org/articles/10.5802/aif.2606/
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