Let $\phi: \chi \to B$ be a proper holomophic submersion with smooth fiber $X$.

Then, we get local systems $R^i \phi_* \mathbb C$ and corresponding flat connection $(B, \bigtriangledown)$

In this case,there are tons of beautiful constructions even in such an elementary level:

infinitesimal VHS, Mixed Hodge structure, Period mapping $P^{n,k} : B \to Grass(b^{n,k}, H^n(X, \mathbb C)), $ Picard-Lefschetz monosromy representation $\rho: \pi_1(B, b_0) \to GL(n, \mathbb C) $ and so on.

But my knowledge of these topic remains too abstract to digest it well. So i am collecting enlightening toy examples. For example, I've worked with the Legendre family of elliptic curves

{$y^2=x(x-1)(x-\lambda)$} $ \to $ {$\mathbb C -(0,1)$}

and interpreted everything into a concrete term.(and it was fantastic)

But i still wants more. Because in my examples, no mixed Hodge structure, no Hodge structure of weight $\ge$ 2. If you have any other good examples, please tell me. Good reference will be extremly helpful. I also appreciate any suggestion.