The aim of this fisrt part is to introduce, for a rather large class of hypersurface singularities with 1 dimensionnal locus, the analog of the Brieskorn lattice at the origin (the singular point of the singular locus). The main results are the finitness theorem for the corresponding (a,b)-module obtained via Kashiwaras constructibility theorem, and non torsion results for a plane curve singularity (not nessarily reduced) and for the suspension of such non torsion cases with an isolated singularity.
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