= Hirzebruch–Jung resolution
{c}
= Minimal resolution of a cyclic quotient surface singularity
{synonym}
For the <cyclic quotient surface singularity> $\frac1r(1,q)$, expand $r/q=[b_1,\ldots,b_s]^-$ with $b_i\ge2$. In the quotient lattice, start with $v_0=(0,1)$, $v_1=(1,q)/r$, and set $v_{i+1}=b_iv_i-v_{i-1}$. The last vector is $(1,0)$, each consecutive pair is a lattice basis, and subdivision by these rays is a resolution. Its exceptional chain has self-intersections $-b_i$. None is a minus-one curve, so the resolution is minimal. All coefficients are two exactly for $q=r-1$.
// Target: geometry-and-topology.bigb
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