With the notation in Example 3.65, consider the standard simplex $\Delta^{n}$ with fan $\Sigma=\Sigma_{\Delta^{n}}$ and support function $\Psi=\Psi_{\Delta^{n}}$. The corresponding toric variety is $X_{\Sigma}=\mathbb{P}^{n}$ with toric line bundle $L_{\Psi}=\mathcal{O}(1)$ and toric section $s_{\Psi}=s_{\infty}$.

1. (1)

   The canonical metrics $\|\cdot\|_{{\operatorname{can}}}$ in examples 2.25 and 2.32 are toric and both correspond to the function $\psi_{\|\cdot\|_{{\operatorname{can}}}}=\Psi$.

2. (2)

   The Fubini-Study metric $\|\cdot\|_{{\operatorname{FS}}}$ in Example 2.2 is also toric and corresponds to the differentiable function $\psi_{\|\cdot\|_{{\operatorname{FS}}}}=f_{{\operatorname{FS}}}$ introduced in Example 3.53.