Questions tagged [belyi]

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Explicit formulas Belyi maps for a rational dessin d'enfants

What are the best references for finding explicit formulas for Belyi maps for rational dessin d'enfants? I am most interested in a formula for the Belyi map that corresponds to a specific rational ...
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3 votes
1 answer

When do tamely ramified Belyi maps exist in characteristic p?

Let $p$ be a prime. Let $d$ be a number. Let $\lambda_0,\lambda_1,\lambda_{\infty}$ be three partitions of $d$ whose parts are prime to $p$. Consider the following question: Does there exist a finite ...
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18 votes
2 answers

Belyi functions on non-compact surfaces; or: Building Riemann surfaces from equilateral triangles

Some background on (compact) Belyi surfaces $\newcommand{\Ch}{\hat{\mathbb{C}}}$ A compact Riemann surface $X$ is called a Belyi surface if there exists a branched covering map $f:X\to \Ch$ such that $...
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4 votes
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technical question about a paper on Belyi's theorem

I'm trying to understand Belyi's theorem, as presented here: He defines a curve $X$ over a field $C$ to be a smooth projective geometrically connected ...
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33 votes
4 answers

Curves which are not covers of P^1 with four branch points

The following interesting question came up in a discussion I was having with Alex Wright. Suppose given a branched cover C -> P^1 with four branch points. It's not hard to see that the field of ...
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