 Cyclic quotient surface singularity

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