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