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Journal of the London Mathematical Society Advance Access originally published online on September 1, 2007
Journal of the London Mathematical Society 2007 76(1):211-224; doi:10.1112/jlms/jdm027
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© 2007 London Mathematical Society

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

Daniel Barlet

Université Henri Poincaré (Nancy I) et Institut Universitaire de France
Institut E. Cartan UHP/CNRS/INRIA
UMR 7502
BP 239
54506 Vandoeuvre-les-Nancy cedex
France

Morihiko Saito

RIMS Kyoto University
Kyoto 606-8502
Japan
msaito{at}kurims.kyoto-u.ac.jp

We study the Brieskorn modules associated to a germ of a holomorphic function with non-isolated singularities and show that the Brieskorn module has naturally the structure of a module over the ring of microdifferential operators of non-positive 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 a sufficient condition for the finiteness is given here. A Thom–Sebastiani-type theorem for the sheaf of Brieskorn modules is also proved when one of two functions has an isolated singularity.

barlet{at}iecn.u-nancy.fr

2000 Mathematics Subject Classification 32S40.

Received November 20, 2004; revised September 6, 2006; published online September 1, 2007.


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