Corollary 6.21 . [02WE]

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Corollary 6.21.

Let $\Sigma$ be a complete fan on $N_{\mathbb{R}}$ and ${\overline{L}}_{i}=(L_{i},\|\cdot\|_{i})$ , $i=0,\dots,n$ , be toric line bundles on $X_{\Sigma}$ generated by global sections and equipped with approachable toric metrics. Choose toric sections $s_{i}$ of $L_{i}$ and let $\Psi_{i}$ be the corresponding support functions. Then the toric height of $X_{\Sigma}$ with respect to ${\overline{L}}_{0},\dots,{\overline{L}}_{n}$ is given by

\operatorname{h}^{\operatorname{tor}}_{{\overline{L}}_{0},\dots,{\overline{L}}_{n}}(X_{\Sigma})=\operatorname{MI}_{M}(\vartheta_{\|\cdot\|_{0}},\dots,\vartheta_{\|\cdot\|_{n}})=\lambda_{K}\operatorname{MI}_{M}(\psi_{\|\cdot\|_{0}}^{\vee},\dots,\psi_{\|\cdot\|_{n}}^{\vee}).