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

Abstract

Following Craw, Maclagan, Thomas and Nakamura's work [Nak01],[CMT07b] on Hilbert schemes for abelian groups, we give an explicit description of the Hilb G C 3 scheme for G = diag(ε, ε a , ε r−a ) by a classification of all G−sets. We describe how the combinatorial properties of the fan of Hilb G C 3 relates to the Euclidean algorithm.