Fujiki-Oka Resolution for Three-dimensional Cyclic Quotient Singularities via Binary Trees

Abstract

For three dimensional cyclic quotient singularities of type $\frac{1}{r}\left(1,a,r-a-1\right)$ (resp. type $\frac{1}{r}\left(1,a,r-a\right)$), the Fujiki-Oka resolution coincides with one of crepant resolutions (resp. an economic resolution). In this paper, we will characterize binary trees which gives the Fujiki-Oka resolution for the above two series of cyclic quotient singularities.