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On the Hodge filtration of Hodge modules. (English) Zbl 1196.14015
The generating level of the Hodge filtration on a pure Hodge module \(M\) is a positive integer measuring the complexity of this filtration. The author obtains an upper bound of this invariant in terms of the dimension of the support of \(M\) and the level of the generic variation of Hodge structure associated to \(M\).
This results disproves in particular Brylinski’s conjecture on the Hodge filtration of a pure Hodge module.

14D07 Variation of Hodge structures (algebro-geometric aspects)
32S35 Mixed Hodge theory of singular varieties (complex-analytic aspects)
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