Pushforward of structure sheaf and virtual global generation
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866909395299860480 |
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| author | Biswas, Indranil Kumar, Manish Parameswaran, A. J. |
| author_facet | Biswas, Indranil Kumar, Manish Parameswaran, A. J. |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2403_15231 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Pushforward of structure sheaf and virtual global generation Biswas, Indranil Kumar, Manish Parameswaran, A. J. Algebraic Geometry 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. |
| title | Pushforward of structure sheaf and virtual global generation |
| topic | Algebraic Geometry |
| url | https://arxiv.org/abs/2403.15231 |