Definition 6.32 . [02WR]

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Definition 6.32.

Let $Y$ be a $d$ -dimensional cycle of $X_{\Sigma}$ . The toric height of $Y$ with respect to ${\overline{L}}_{0},\dots,{\overline{L}}_{d}$ is

\operatorname{h}^{\operatorname{tor}}_{{\overline{L}}_{0},\dots,{\overline{L}}_{d}}(Y)=\sum_{v\in\mathfrak{M}_{\mathbb{K}}}n_{v}\operatorname{h}^{\operatorname{tor}}_{{\overline{L}}_{0}^{v},\dots,{\overline{L}}_{d}^{v}}(Y)\in\mathbb{R}.