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

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

2004-11-18

arxiv.org/abs/math/0411406v2

Mathematics

Complex Variables

16 pages

Scientific paper

We study the Brieskorn modules associated to a germ of holomorphic function with non-isolated singularities, and show that the Brieskorn module has naturally a structure of a module over the ring of microdifferential operators of nonpositive degree, and that the kernel of the morphism to the Gauss-Manin system coincides with the torsion part for the action of $t$ and also with that for the action of 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 sheaf of Brieskorn modules in the case one of two functions has an isolated singularity.

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