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arXiv · 2604.18782

On the Hurwitz existence problem for branched covers of the projective line

Ciro Ciliberto·Andreas Leopold Knutsen·Sara Torelli
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Abstract

We give an alternative proof of the Hurwitz existence problem for branched covers of $\mathbb{P}^1$ in the case where the number of ramification points equals the number of branch points, that is, where all the ramification profiles are of the form $[e,1,\ldots,1]$ with $e \geq 2$.

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Ciro Ciliberto, Andreas Leopold Knutsen, Sara Torelli. 2026-04-20. On the Hurwitz existence problem for branched covers of the projective line. https://arxiv.org/abs/2604.18782

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