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arXiv · 2403.15231

Pushforward of structure sheaf and virtual global generation

Indranil Biswas·Manish Kumar·A. J. Parameswaran
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Abstract

Let $f:X\rightarrow Y$ 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.

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Indranil Biswas, Manish Kumar, A. J. Parameswaran. 2024-03-22. Pushforward of structure sheaf and virtual global generation. https://doi.org/10.1017/s001309152400021x

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