Consider a variation of polarized Hodge structure on a punctured disk. Suppose that connection preserves Hodge filtration (which is much stronger, than Griffiths transversality). Moreover assume that that monodromy is unipotent.

Question: Is monodromy trivial?

This question appeared during reading paragraph 4 of [classical paper][1].




  [1]: http://www.maths.ed.ac.uk/~aar/papers/schmid.pdf