Proposition 5.18.2`AB08C5138082`

Proposition 5.18.2.AB08C5138082 Let $\varphi ,\psi \in \mathrm{QPSH}(X)$ be potentials with analytic singularities. Then so are $\lambda \varphi $ ($\lambda \in \mathbb {Q}_{>0}$), $\varphi +\psi $ and $\varphi \lor \psi $.

Proof. The assertion for $\lambda \varphi $ follows by multiplying the rational coefficient in (5.18.1). The assertion for $\lor $ is proved in [Proposition 4.1.8, Dem15]. For the addition assertion, take local presentations as in (5.18.1) and multiply the corresponding finite systems of holomorphic generators. $\square$

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@misc{pome-tag-AB08C5138082,
  author = {{Pome contributors}},
  title = {Proposition 5.18.2},
  howpublished = {Pome},
  url = {https://mingchenxia.github.io/Pome/tag/AB08C5138082/}
}

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Proposition 5.18.2AB08C5138082

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Proposition 5.18.2`AB08C5138082`