Abstract
Given a nonzero germ h of holomorphic function on (C n ,0), we study condition: the ideal AnnD 1/h is generated by operators of order 1. When h defines a generic arrangement of hypersurfaces with an isolated singularity, we show that it is verified if and only if h is weighted homogeneous and −1 is only integral root of its Bernstein-Sato polynomial. When h is a product, we give a process to test this last condition. Finally, we study some other related conditions.
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