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Pushforward of structure sheaf and virtual global generation
Published online by Cambridge University Press: 18 April 2024
Abstract
Let $f\,:\,X\,\longrightarrow \,Y$ be a generically smooth morphism between irreducible smooth projective curves over an algebraically closed field of arbitrary characteristic. We prove that the vector bundle
$((f_*{\mathcal O}_X)/{\mathcal O}_Y)^*$ is virtually globally generated. Moreover,
$((f_*{\mathcal O}_X)/{\mathcal O}_Y)^*$ is ample if and only if f is genuinely ramified.
MSC classification
- Type
- Research Article
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- © The Author(s), 2024. Published by Cambridge University Press on Behalf of The Edinburgh Mathematical Society.