Quelques résultats sur certaines fonctions à lieu singulier de dimension 1

This text is a survey on my recent work [B.04] on some holomorphic germs having a one dimensional singular locus. An analogous of the Brieskorn module of an isolated singularity is defined and a finiteness theorem is proved using Kashiwara’s constructibility theorem. A bound for the (finite dimensional) torsion is also obtained. Non existence of torsion is proved for curves (reduced or not) an this property is stable by “Thom-Sebastiani” adjunction of an isolated singularity. This provides a lot of examples in any dimension where our formula r = μ(f)+v(f) generalizing the Milnor number formula, is valid.