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Following Craw, Maclagan, Thomas and Nakamura's work on Hilbert schemes forabelian groups, we give an explicit description of the G-Hilbert scheme for Gequal to a cyclic group of order r, acting on C^3 with weights 1,a,r-a. Wedescribe how the combinatorial properties of the fan of G-Hilbert schemerelates to the Euclidean algorithm.

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