Lemma 5.43.24`83C3A394E5BB`

Lemma 5.43.24.83C3A394E5BB For a proper bimeromorphic map $\rho :Z\to Y$ between complex manifolds and quasi-plurisubharmonic functions $a,b$ on $Y$,

\[ a\sim _{\mathcal I}b \quad \Longleftrightarrow \quad a\circ \rho \sim _{\mathcal I}b\circ \rho . \]

The statement is local on $Y$.

Proof. Apply the local order equivalence of lemma 5.43.23 to both $(a,b)$ and $(b,a)$. Together, the two order relations are equivalent to equality of the multiplier ideals at every positive weight. $\square$

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BibTeX citation

@misc{pome-tag-83C3A394E5BB,
  author = {{Pome contributors}},
  title = {Lemma 5.43.24},
  howpublished = {Pome},
  url = {https://mingchenxia.github.io/Pome/tag/83C3A394E5BB/}
}

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Lemma 5.43.2483C3A394E5BB

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Lemma 5.43.24`83C3A394E5BB`