Lemma 1.2 . [01DT]

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Lemma 1.2.

Assume that $\mathcal{L}\in\Pic(\mathcal{X})$ is nef on $\mathcal{X}_{0}$ , i.e. $\mathcal{L}\cdot C\geq 0$ for all $k$ -proper curves $C$ in $\mathcal{X}_{0}$ . Then $\mathcal{L}$ is also nef on $\mathcal{X}_{K}$ , i.e. $\mathcal{L}\cdot C\geq 0$ for all $K$ -proper curves $C$ of $\mathcal{X}_{K}$ as well.