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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 \(h\).

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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