Brieskorn modules and Gauss-Manin systems for non isolated hypersurface singularities
Résumé
We study the Brieskorn modules associated to a function with non isolated singularities, and show that the kernel of the morphism to the Gauss-Manin system coincides with the torsion part for the action of $t$ and also for the inverse of the Gauss-Manin connection. This torsion part is not finitely generated in general, and we give a sufficient condition for the finiteness. We also prove a Thom-Sebastiani type theorem for the Brieskorn modules in the case one of two functions has an isolated singularity.