Pierre Deligne in his celebrated paper entitling "Local behavior of Hodge structures at infinity" introduced Maximal degenerations of Calabi-Yau manifolds.

Let $\pi:X\to \mathbb C^*$ be a family of degeneration of of Calabi-Yau fibers. We have from D. Barlet asymptotic formula

$$\int_{X_s}\Omega_s\wedge\bar\Omega_s=C(\log |s|)^m|s|^{2k}(1+O(1))$$

for some $C \in \mathbb C^∗$, $k ∈ \mathbb Z, 0 \leq m \leq n = dim(X)$

We say that $X$ has maximal degeneration at $s = 0$, if in the formula above we have $m = n$.

Later this definition become important in Miror symmetry. I am woundring if is there any example for special case when maximal degeneration on moduli space of Calabi-Yau fibers happen.