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Apr 3, 2021 at 5:42 comment added abx @Will Sawin: Very interesting question! Unfortunately I have no idea...
Apr 3, 2021 at 0:53 comment added Will Sawin Do you think that for each $g$ and each $0<k<3g-3$ (i.e. avoiding this case and Belyi case) it's open whether every curve of genus $g$ defined over an algebraically closed field of transcendence degree $k$ has a map to $\mathbb P^1$ branched over at most $k+3$ points?
Apr 2, 2021 at 18:41 vote accept Lasse Rempe
Apr 2, 2021 at 18:22 history answered abx CC BY-SA 4.0