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

Ciro Ciliberto; Andreas Leopold Knutsen; Sara Torelli

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

Algebraic Geometry 2026-05-06 v2

Authors: Ciro Ciliberto , Andreas Leopold Knutsen , Sara Torelli

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 $e \geq 2$ .

Keywords

Hurwitz existence problem branched covers projective line ramification profiles Riemann-Hurwitz formula monodromy

Cite

@article{arxiv.2604.18782,
  title  = {On the Hurwitz existence problem for branched covers of the projective line},
  author = {Ciro Ciliberto and Andreas Leopold Knutsen and Sara Torelli},
  journal= {arXiv preprint arXiv:2604.18782},
  year   = {2026}
}

Comments

We were informed that the main theorem had already been proved by Chenakkod, Faraco and Gupta, so we have added this reference and changed the abstract and introduction accordingly

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

Abstract

Keywords

Cite

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