Quelques résultats sur certaines fonctions à lieu singulier de dimension 1

Daniel Barlet (1, 2)

1 IECN - Institut Élie Cartan de Nancy
2 IUF - Institut universitaire de France

This next is a survey on my recent work [B.04] on some holomorphic germs having a one dimensional singular locus. An analoguous of the Brieskorn module of an isolated singularity is defined and a finitness 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) and this property is stable by "Thom-Sebastiani" adjunction of an isolated singularity. This provides a lot of examples in any dimension.

Mots clés: Hypersurface singularity; 1 dimensional singular locus; Brieskorn module; (a; b)-module; formal microlocal operators

Domaines: Variables complexes [math.CV]

Daniel Barlet. Quelques résultats sur certaines fonctions à lieu singulier de dimension 1. 2006. ⟨hal-00102131⟩