PomeCorollary 20.2.49.50ABF7A3834B Let $\varphi \in \mathrm{QPSH}(X)$. Then for quasi-every $H\in \Lambda $, we have $\varphi |_ H\not\equiv -\infty $.
Corollary 20.2.4950ABF7A3834B
Proof. For quasi-every $H$, theorem 20.2.45 gives
\[ \mathcal I(\varphi |_ H)=\operatorname{Res}_ H\mathcal I(\varphi ). \]
After removing the hyperplanes meeting the associated points of $\mathcal O_ X/\mathcal I(\varphi )$ improperly, the right-hand side is non-zero. Since $\mathcal I(-\infty )=0$, this implies $\varphi |_ H\not\equiv -\infty $. $\square$
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