Proposition 20.1.49`FE8A163BAA22`

Proposition 20.1.49.FE8A163BAA22 The product in definition 20.1.41 is continuous along decreasing nets in each variable. In other words, if $(\mathbb {D}_ i^ j)_{j\in J}$ ($i=1,\ldots ,n$) are decreasing nets of nef b-divisors over $X$ with limits $\mathbb {D}_ i$, then

\[ \lim _{j\in J} \left(\mathbb {D}_1^ j,\ldots ,\mathbb {D}_ n^ j\right)=\left(\mathbb {D}_1,\ldots ,\mathbb {D}_ n\right). \]

Proof. This is a straightforward consequence of 20.1.40 4 and proposition 20.1.47. $\square$

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BibTeX citation

@misc{pome-tag-FE8A163BAA22,
  author = {{Pome contributors}},
  title = {Proposition 20.1.49},
  howpublished = {Pome},
  url = {https://mingchenxia.github.io/Pome/tag/FE8A163BAA22/}
}

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Proposition 20.1.49FE8A163BAA22

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Proposition 20.1.49`FE8A163BAA22`