Bernstein polynomials and spectral numbers for linear free divisors

Sevenheck, Christian

Annales de l'Institut Fourier, Tome 61 (2011) no. 1, pp. 379-400.

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.

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.

Classification : 32S40, 34M35
Keywords: Brieskorn lattice, Bernstein polynomial, linear free divisors, spectral numbers
Mot clés : réseau de Brieskorn, polynôme de Bernstein, diviseur linéairement libre, nombres spectraux

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