On meromorphic functions defined by a differential system of order 1, II

Details On meromorphic functions defined by a differential system of order 1, II On meromorphic functions defined by a differential system of order 1, II

2006-05-31

arxiv.org/abs/math/0605787v1

Mathematics

Algebraic Geometry

28 pages, 1 diagram

Scientific paper

Given a nonzero germ h of holomorphic function on (C^n,0), we study the condition: ``the ideal Ann\_D 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 the 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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