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Let $\pi: X \to \Delta^*$ be a smooth, projective morphism. We know that for each $k$, there is a natural local system $L:=R^k \pi_*\mathbb{C}$. The associated vector bundle $\mathcal{L}:=L \otimes \...

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 ...