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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.

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