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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 $C \in \mathbb C^∗$, $k ∈ \mathbb Z, 0 \leq m \leq n = dim(X)$ and we can formulate $m$ via log-canonical threshold, see Proposition 2.1 of this paper

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 ?

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

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 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 ?

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 $C \in \mathbb C^∗$, $k ∈ \mathbb Z, 0 \leq m \leq n = dim(X)$ and we can formulate $m$ via log-canonical threshold, see Proposition 2.1 of this paper

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 ?

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 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 when maximal degeneration on moduli space of Calabi-Yau fibers happen.

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 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 ?