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.
We would like to thank Professor Tadashi Ashikaga for dedicated support, especially, helpful discussions at Tohokugakuin University. We also thank Professor Yukari Ito and Professor Alastair Craw for giving us many useful advices. National Institute of Technology, Oyama college has supported our study.
"Crepant Property of Fujiki-Oka Resolutions for Gorenstein Abelian Quotient Singularities." Nihonkai Math. J. 32 (1) 41 - 69, 2021.