Structures de Hodge mixtes associées à un germe de fonction à point critique isolé. (French) Zbl 0555.32018

Astérisque 101/102, 268-285 (1983).
The vanishing cohomology groups of a germ of holomorphic function with isolated critical point carry a mixed Hodge structure; A. Varchenko has shown how to construct a filtration \(F'_ a\) which induces the Hodge filtration on the graded space with respect to the weight filtration; his description does not use the resolution of singularities. In a preprint ”On the mixed Hodge structure on the cohomology of the Milnor fibre”, J. Scherk and the reviewer have attempted to give a resolution-free description of the Hodge filtration; the paper under review shows how to overcome the difficulties in this preprint by using the theory of \({\mathcal D}\)-modules. It uses the author’s Gauss-Manin system and incorporates a remark made by M. Saito about the necessity to pass to a finite covering to obtain unipotent monodromy. A corrected version of the paper by J. Scherk and the reviewer appears in Math. Ann. 271, 641-665 (1985).
For the entire collection see [Zbl 0515.00021].
Reviewer: J.H.M.Steenbrink


32J25 Transcendental methods of algebraic geometry (complex-analytic aspects)
32B10 Germs of analytic sets, local parametrization
14C30 Transcendental methods, Hodge theory (algebro-geometric aspects)
32S05 Local complex singularities