Example 22.1.13796F447D96B6

Example 22.1.13.796F447D96B6 Fix $\varphi \in \mathrm{PSH}(X,\theta )$. We can define an associated non-Archimedean metric

as follows:

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   $\Gamma ^{\varphi }_{\max }=0$;

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   for any $\omega \in \textup{Käh}(X)$ and any $\tau <0$, we set

   \[ \Gamma ^{\varphi ,\theta +\omega }_{\tau }=P_{\theta +\omega }[\varphi ]_{\mathcal{I}}. \]

Such non-Archimedean metrics are called homogeneous non-Archimedean metrics.

Observe that

See proposition 18.1.27 and the footnote there.