= Cyclic quotient surface singularity
{title2=$\frac1r(1,q)$}
For $r>1$ and $\gcd(r,q)=1$, the quotient of $\mathbb A^2$ by $(x,y)\mapsto(\zeta x,\zeta^q y)$ is a cyclic quotient surface singularity. Its toric model uses the first-quadrant cone in $\mathbb Z^2+\mathbb Z(1,q)/r$. Conversely, every singular full-dimensional affine toric surface over an algebraically closed field of characteristic zero has this form. Smooth cones and cones with a torus factor require separate treatment.
// Target: geometry-and-topology.bigb
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