Hilbert desingularizations for three dimensional canonical cyclic quotient singularities

Abstract

In this paper, we shall discuss Hilbert property of ${\mathrm{Hilb}}^G({\mathbb{C}}^3)$, Fujiki-Oka resolutions and iterated Fujiki-Oka resolutions for three dimensional canonical cyclic quotient singularities by using the classification shown by Ishida and Iwashita\cite{II}. Finally, we shall prove that there exists a Hilbert desingularization for any three dimensional canonical cyclic quotient singularity.

11 pages, 3 figures