# Questions tagged [belyi]

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5
questions

**6**

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**2**answers

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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 ...

**3**

votes

**1**answer

309 views

### 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 ...

**16**

votes

**2**answers

908 views

### 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 ...

**4**

votes

**1**answer

472 views

### technical question about a paper on Belyi's theorem

I'm trying to understand Belyi's theorem, as presented here: http://eprints.soton.ac.uk/29785/1/b45h1koe.pdf
He defines a curve $X$ over a field $C$ to be a smooth projective geometrically connected ...

**33**

votes

**4**answers

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### 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 ...