Direct image of structure sheaf and parabolic stability
Fuente:
arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866913541835980800 |
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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 dominant generically smooth morphism between irreducible smooth projective curves over an algebraically closed field $k$ such that ${\rm Char}(k)> \text{degree}(f)$ if the characteristic of $k$ is nonzero. We prove that $(f_*{\mathcal O}_X)/{\mathcal O}_Y$ equipped with a natural parabolic structure is parabolic polystable. Several conditions are given that ensure that the parabolic vector bundle $(f_*{\mathcal O}_X)/{\mathcal O}_Y$ is actually parabolic stable. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2410_08528 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Direct image of structure sheaf and parabolic stability Biswas, Indranil Kumar, Manish Parameswaran, A. J. Algebraic Geometry Let $f : X \rightarrow Y$ be a dominant generically smooth morphism between irreducible smooth projective curves over an algebraically closed field $k$ such that ${\rm Char}(k)> \text{degree}(f)$ if the characteristic of $k$ is nonzero. We prove that $(f_*{\mathcal O}_X)/{\mathcal O}_Y$ equipped with a natural parabolic structure is parabolic polystable. Several conditions are given that ensure that the parabolic vector bundle $(f_*{\mathcal O}_X)/{\mathcal O}_Y$ is actually parabolic stable. |
| title | Direct image of structure sheaf and parabolic stability |
| topic | Algebraic Geometry |
| url | https://arxiv.org/abs/2410.08528 |