Corollary 11.12.7`2984296C9B5A`

Corollary 11.12.7.2984296C9B5A Let $F$ be the underlying smooth bundle of $F_0$ in theorem 11.9.4, with a holomorphic structure in the neighborhood given there. If $F^*$ is ample, then $F^*$ admits no strongly pseudoconvex squared Finsler metric with semipositive Kobayashi curvature.

Proof. Apply corollary 11.12.6 to $E=F^*$. Such a metric would produce a smooth complex norm on $F$ with plurisubharmonic square, contrary to theorem 11.9.4. $\square$

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@misc{pome-tag-2984296C9B5A,
  author = {{Pome contributors}},
  title = {Corollary 11.12.7},
  howpublished = {Pome},
  url = {https://mingchenxia.github.io/Pome/tag/2984296C9B5A/}
}

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Corollary 11.12.72984296C9B5A

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Corollary 11.12.7`2984296C9B5A`