Tschirnhausen bundles of sextic covers of $\mathbb{P}^1$
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2026
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| _version_ | 1866910105839075328 |
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| author | Frengley, Sam Vemulapalli, Sameera |
| author_facet | Frengley, Sam Vemulapalli, Sameera |
| contents | A degree $d$ genus $g$ cover of the complex projective line by a smooth irreducible curve $C$ yields a vector bundle on the projective line by pushforward of the structure sheaf. We classify the bundles that arise this way when $d = 6$. Interestingly, our methods show that all constraints on the pushforward are ``explained'' by multiplication in an algebra. Finally, we show that all possible pushforwards are realized by covers with a nontrivial proper subcover. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_04709 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Tschirnhausen bundles of sextic covers of $\mathbb{P}^1$ Frengley, Sam Vemulapalli, Sameera Algebraic Geometry 14H51, 14H10 A degree $d$ genus $g$ cover of the complex projective line by a smooth irreducible curve $C$ yields a vector bundle on the projective line by pushforward of the structure sheaf. We classify the bundles that arise this way when $d = 6$. Interestingly, our methods show that all constraints on the pushforward are ``explained'' by multiplication in an algebra. Finally, we show that all possible pushforwards are realized by covers with a nontrivial proper subcover. |
| title | Tschirnhausen bundles of sextic covers of $\mathbb{P}^1$ |
| topic | Algebraic Geometry 14H51, 14H10 |
| url | https://arxiv.org/abs/2604.04709 |