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arXiv · 2604.04709

Tschirnhausen bundles of sextic covers of $\mathbb{P}^1$

Sam Frengley·Sameera Vemulapalli
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Abstract

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.

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Sam Frengley, Sameera Vemulapalli. 2026-04-06. Tschirnhausen bundles of sextic covers of $\mathbb{P}^1$. https://arxiv.org/abs/2604.04709

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