Let $\pi:\mathcal{X}^{\prime}\to\mathcal{X}$ be a vertical blow-up.

• (i)

  There exists a $\pi$-ample divisor $A\in\Div_{0}(\mathcal{X}^{\prime})$.

• (ii)

  If $\mathcal{L}\in\Pic(\mathcal{X})$ is ample then there exists $m\in\mathbf{N}$ such that $\pi^{*}(m\mathcal{L}|_{\mathcal{X}_{K}})$ extends to an ample line bundle $\mathcal{L}^{\prime}$ on $\mathcal{X}^{\prime}$.