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A neat monodromy group of a family of Kaehler manifolds

Let $G$ be the monodromy group on $H^n(X_b,\mathbb{Z})$, where $n=\dim X_b$ with the smooth fiber $X_b$ over some $b \in B$. … I think my question is false if one removes the geometric picture that the group $G$ is the monodromy group of a family of Kahelr manifolds. …
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