2004/11/18 by Daniel Barlet, Barlet, Daniel, Morihiko Saito +1 · 1 citation
Mathematics · #32S40 #Algebraic Geometry (math.AG) #Complex Variables (math.CV) #FOS: Mathematics #math.AG #math.CV #msc:32S40
paper · pdf · doi:10.48550/arxiv.math/0411406
16 pages
arxiv created 2006/07/05 · arxiv updated 2009/12/01
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.