ScalingStacks

Recall that $\omega_{t}$ denotes the Calabi-Yau metric on $X_{t}$ in the class $\frac{1}{|\log|t||}c_{1}(L)|_{X_{t}}$, and that the dimension $m$ of the essential skeleton of $X$ is assumed to be stricty positive (and necessarily $m\leqslant n$). Denote by $\mu_{t}$ the Calabi-Yau volume form on $X_{t}$ normalized to be a probability measure, i.e.

(2.1)

$$\mu_{t}=\frac{\omega_{t}^{n}}{\int_{X_{t}}\omega_{t}^{n}}=\frac{i^{n^{2}}\Omega_{t}\wedge\overline{\Omega_{t}}}{\int_{X_{t}}i^{n^{2}}\Omega_{t}\wedge\overline{\Omega_{t}}}.$$