Corollary 8.2 . [0183]

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Corollary 8.2.

If ${\mathcal{X}}$ (i.e. the pair $({\mathcal{X}},{\mathcal{X}}_{0,\mathrm{red}})$ ) is dlt, then

\lim_{t\to 0}\frac{\int_{{\mathcal{X}}_{t}}e^{2\psi_{t}}}{|t|^{2\kappa_{\min}}(2\pi\log|t|^{-1})^{d}}=\sum_{\sigma}\left(\int_{Y_{\sigma}}\operatorname{Res}_{Y_{\sigma}}({\mathcal{L}}^{\#})\right)b_{\sigma}^{-1}\operatorname{Vol}(\sigma),

where $\sigma$ runs over the $d$ -dimensional faces of $\Delta({\mathcal{L}})$ .