be the associated holomorphic vector bundle with Gauss-Manin connection $\nabla$ and Hodge filtration $F^\bullet\mathcal H^k$. Choose a marking of the local system $R^k\pi_*\mathbb C$, so that the Hodge filtrations define a local period map
paragraph
admin
\begin{align*}
\Phi:S\to D
\end{align*}
latex_env
admin
to the corresponding polarized period domain $D$. Then, for every $s\in S$,