Let $\Delta=\{z\in\mathbb C: |z|<1\}$ and let $\Delta^*=\Delta\setminus\{0\}$. Let $f:\mathcal X\to\Delta$ be a proper holomorphic Kähler morphism, and suppose that the restricted morphism $f|_{f^{-1}(\Delta^*)}:f^{-1}(\Delta^*)\to\Delta^*$ is smooth. For $t\in\Delta^*$, write $X_t=f^{-1}(t)$. For every integer $k\ge 0$, let