Tag Archives: belyi

There’s no 4-branched Belyi’s theorem — right?

Much discussion on Math Overflow has not resolved the following should-be-easy question:

Give an example of a curve in {\mathcal{M}}_g defined over \bar{Q} which is not a family of 4-branched covers of P^1.

Surely there is one!  But then again, you’d probably say “surely there’s a curve over \bar{Q} which isn’t a 3-branched cover of P^1.”  But there isn’t — that’s Belyi’s theorem.

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