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1 results

Pushforward of structure sheaf and virtual global generation
Part of
- Curves
Indranil Biswas, Manish Kumar, A. J. Parameswaran
Journal:

Proceedings of the Edinburgh Mathematical Society / Volume 67 / Issue 3 / August 2024

Published online by Cambridge University Press:

18 April 2024, pp. 663-673
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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.