Proposition 17.12.15`2059587BD91B`

Proposition 17.12.15.2059587BD91B Let $\pi \colon Y\rightarrow X$ be a proper bimeromorphic morphism from a Kähler manifold $Y$. Then the pointwise pull-back induces a bijection

\[ \pi ^*\colon \mathrm{TC}(X,\theta ;\phi )\xlongrightarrow {\sim } \mathrm{TC}(Y,\pi ^*\theta ;\pi ^*\phi ). \]

Proof. The bijectivity on the underlying potentials follows from proposition 5.17.8. The compatibility with model potentials follows from proposition 16.4.1. These two facts also preserve concavity, monotonicity and the value of $\Gamma _{-\infty }$, hence give the asserted bijection of test curves. $\square$

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@misc{pome-tag-2059587BD91B,
  author = {{Pome contributors}},
  title = {Proposition 17.12.15},
  howpublished = {Pome},
  url = {https://mingchenxia.github.io/Pome/tag/2059587BD91B/}
}

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Proposition 17.12.152059587BD91B

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Proposition 17.12.15`2059587BD91B`