Corollary 20.1.34`5108D6DF4DAE`

Corollary 20.1.34.5108D6DF4DAE There is a canonical bijection between the following two sets:

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The set of

\[ \varprojlim _{\omega } \left( \mathcal{Z}_+(X,\alpha +\omega )_{>0}/\sim _{\mathcal{I}} \right), \]

where $\omega $ runs over the directed set of Kähler forms on $X$;
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the set of augmented nef b-divisors over $X$ with cohomology class $\alpha $.

Proof. Apply corollary 20.1.31 to the non-divisorial parts and use Siu's decomposition on $X$ to record the divisorial part. The convergence condition in definition 20.1.32 is exactly the condition that the roots of the non-divisorial parts converge to the prescribed cohomology class $\alpha $. $\square$

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@misc{pome-tag-5108D6DF4DAE,
  author = {{Pome contributors}},
  title = {Corollary 20.1.34},
  howpublished = {Pome},
  url = {https://mingchenxia.github.io/Pome/tag/5108D6DF4DAE/}
}

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Corollary 20.1.345108D6DF4DAE

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Corollary 20.1.34`5108D6DF4DAE`