Nihonkai Math. J. 32 (1), 41-69, (2021)
KEYWORDS: Crepant resolutions, Fujiki-Oka resolutions, multidimensional continued fractions, Hirzebruch-Jung continued fractions, quotient singularities, Higher dimension, finite groups, Abelian groups, toric varieties, invariant theory, 14B05, 14J17, 13H10, 14C17, 14J30, 14J35, 14J40, 14L30, 14M25, 52B20
We show a necessary and sufficient condition for the Fujiki-Oka resolutions of Gorenstein abelian quotient singularities to be crepant in all dimensions by using Ashikaga’s continued fractions. Moreover, we prove that any three dimensional Gorenstein abelian quotient singularity possesses a crepant Fujiki-Oka resolution as a corollary. This alternative proof of existence needs only simple computations compared with the results ever known.