Brieskorn modules and Gauss-Manin systems for non isolated hypersurface singularities

Daniel Barlet (1, 2)

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

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.

Mots clés: Brieskorn Modules; non isolated hypersurface singularities

Domaines: Variables complexes [math.CV]

Daniel Barlet. Brieskorn modules and Gauss-Manin systems for non isolated hypersurface singularities. 2007. ⟨hal-00102152⟩