The G-Hilbert scheme for 1/r(1,a,r-a)

Following Craw, Maclagan, Thomas and Nakamuras work on Hilbert schemes for abelian groups, we give an explicit description of the G-Hilbert scheme for G equal to a cyclic group of order r, acting on C^3 with weights 1,a,r-a. We describe how the combinatorial properties of the fan of G-Hilbert scheme relates to the Euclidean algorithm.