Geodesic
On the Resolution Diagrams of the Brieskorn Singularities (2,q,r) of Type II
Canadian journal of mathematics, Tome 35 (1983) no. 6, pp. 1049-1058

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Let p, q, r be pairwise coprime integers with 2 ≦ p < q < r. The equation defines a complex hypersurface V(p, q, r) ⊂ C 3 which has an isolated singular point at the origin. We call the singularity the Brieskorn singularity (p, q, r). An algorithm of resolving this singularity is known [1]. According to the algorithm, the resolution diagram which describes the configuration of the pre-image of the singular point in the resolved surface is a star-shaped tree Γp, q, r with three branches: 1.1 The positive integers (weights) ai, bj, ck are given as follows: Let x, y, z, b be integers satisfying 1.2 
Yamada, Akio; Matsumoto, Yukio. On the Resolution Diagrams of the Brieskorn Singularities (2,q,r) of Type II. Canadian journal of mathematics, Tome 35 (1983) no. 6, pp. 1049-1058. doi: 10.4153/CJM-1983-058-0
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