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On meromorphic functions defined by a differential system of order 1. (English) Zbl 1080.32011
Summary: Given a germ h of holomorphic function on $$(\mathbb C^n,0)$$, we study the condition: “the ideal $$\text{Ann}_{{\mathcal D}}1/h$$ is generated by operators of order”. We obtain here full characterizations in the particular cases of Koszul-free germs and unreduced germs of plane curves. Moreover, we prove that this condition holds for a special type of hyperplane arrangements. These results allow us to link this condition to the comparison of de Rham complexes associated with $$h$$.

##### MSC:
 32C38 Sheaves of differential operators and their modules, $$D$$-modules 14F10 Differentials and other special sheaves; D-modules; Bernstein-Sato ideals and polynomials 32S25 Complex surface and hypersurface singularities 14F40 de Rham cohomology and algebraic geometry
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