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

Abstract

Following Craw, Maclagan, Thomas and Nakamura's 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.

17 pages, 1 figure; to appear in Glasgow Mathematical Journal

Cited by in corpus (2)

• Hilbert desingularizations for three dimensional canonical cyclic quotient singularities
• Danilov resolution and representations of McKay quiver