ScalingStacks

We say the degeneration family is Calabi-Yau if there is a trivialising section $\Omega$ of the canonical bundle $K_{X}$. Over a small disc $\mathbb{D}_{t}$ around $0\in S$, this induces holomorphic volume forms $\Omega_{t}$ on $X_{t}$ via $\Omega=dt\wedge\Omega_{t}$. The normalised Calabi-Yau measure on $X_{t}$ is the probability measure

$$d\mu_{t}=\frac{\Omega_{t}\wedge\overline{\Omega}_{t}}{\int_{X_{t}}\Omega_{t}\wedge\overline{\Omega}_{t}}.$$

(2)