Theorem B.1 (Kodaira vanishing) . [01HU]

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Theorem B.1 (Kodaira vanishing).

Let $\mathcal{X}$ be an SNC $S$ -variety and $\mathcal{L}\in\Pic(\mathcal{X})$ an ample line bundle. Then we have

H^{q}\left(\mathcal{X},\omega_{\mathcal{X}}\otimes\mathcal{L}\right)=0\quad\text{for all $q\geq 1$}.