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

We study the Brieskorn modules associated to a germ of a holomorphicfunction with non-isolated singularities and show that the Brieskornmodule has naturally the structure of a module over the ringof microdifferential operators of non-positive degree, and thatthe kernel of the morphism to the Gauss–Manin system coincideswith the torsion part for the action of t and also with thatfor the action of the inverse of the Gauss–Manin connection.This torsion part is not finitely generated in general, anda sufficient condition for the finiteness is given here. A Thom–Sebastiani-typetheorem for the sheaf of Brieskorn modules is also proved whenone of two functions has an isolated singularity.