Sur les germes de fonctions holomorphes a lieu singulier de dimension 1: le cas général.

Daniel Barlet (1, 2)

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

The main goal of this article is to extend the results of [B.06] to a general holomorphic germ $f$ with a one dimensional singular locus at the origine of $\Bbb C ^{n+1}, n ≥ 2$. To obtain this generalization it is enough to prove that some nice properties of the cohomology sheaves of the formal completion "in $f$" of the sub-complex given by holomorphic forms annihilated by $\wedge df$ of the holomorphic de Rham complex, obtained under the assumption (HH) in [B.06] are true in general. We also compute explicitely some examples and show the relationship between the $(a,b)$-connexion introduced previously and integrals "à la Malgrange" on vanishing cycles.

Mots clés: Hypersurface; Non Isolated Singularity; Vanishing Cycles; (a; b)-modules.; b)-modules

Domaines: Variables complexes [math.CV]

Daniel Barlet. Sur les germes de fonctions holomorphes a lieu singulier de dimension 1: le cas général.. 2007. ⟨hal-00124034⟩