Corollary 21.13.42`B202075FB15E`

Corollary 21.13.42.B202075FB15E Let $E$ be a $T$-invariant prime divisor on $X$ corresponding to a ray $\rho \in \Sigma (1)$. Then for any $\varphi \in \mathrm{PSH}_{\mathrm{tor}}(X,\theta )_{>0}$, we have

\[ \nu (\varphi ,E)=\inf \left\{ \langle m-m_{\rho },u_{\rho }\rangle : m\in \Delta (\theta ,\varphi ) \right\} . \]

Proof. This follows immediately from theorem 21.13.39 and theorem 19.4.51. In fact, since $X$ is projective and smooth, there is always a $T$-invariant smooth flag $Y_{\bullet }$ with $Y_1=E$. $\square$

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@misc{pome-tag-B202075FB15E,
  author = {{Pome contributors}},
  title = {Corollary 21.13.42},
  howpublished = {Pome},
  url = {https://mingchenxia.github.io/Pome/tag/B202075FB15E/}
}

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Corollary 21.13.42B202075FB15E

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Corollary 21.13.42`B202075FB15E`