Let $\pi:X\to \mathbb C^*$ be a family of degeneration of of Calabi-Yau fibers. We have from D. Barlet asymptotic formula
for some $C \in \mathbb C^∗$, $k ∈ \mathbb Z, 0 \leq m \leq n = dim(X)$ and we can formulate $m$ via log-canonical threshold, see Proposition 2.1 of this paper of Mourougane
In another view we want the degeneracy index $m=δ(X,X_0)$ defined by Halle–Nicaise be exactly $n=dim X$
We say that $X$ has maximal degeneration at $s = 0$, if in the formula above we have $m = n$.
Later this definition become very important in Miror symmetry for example in Siebert-Gross program or Kontsevich-Soibelman program.
I am woundring if there is any concrete example for maximal degeneration on moduli space of Calabi-Yau fibers. Moreover, which properties are known that central fiber $X_0$ must have , to get such maximal degeneration ?