On the mixed Hodge structure on the cohomology of the Milnor fibre. (English) Zbl 0618.14002

The aim of the paper under review is to introduce a mixed Hodge structure on the cohomology of the Milnor fibre of an isolated hypersurface singularity. Such an attempt was already done earlier in 1976 [see J. H. M. Steenbrink in Real and complex singularities, Proc. Nordic Summer Sch., Symp. Math., Oslo 1976, 525-563 (1977; Zbl 0373.14007)] by using completely different methods. The main difference here is that the authors use the theory of holonomic D-modules in one variable with regular singularity (instead of using the resolution of singularities). This second approach has the advantage that one can better understand the Hodge filtration and it is more suited for applications. At the end of the paper the mixed Hodge structure is explicitly computed on two examples.
Reviewer: L.Bădescu


14C30 Transcendental methods, Hodge theory (algebro-geometric aspects)
14J17 Singularities of surfaces or higher-dimensional varieties
14B05 Singularities in algebraic geometry
32S05 Local complex singularities


Zbl 0373.14007
Full Text: DOI EuDML


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