Crepant Property of Fujiki-Oka Resolutions for Gorenstein Abelian Quotient Singularities

2020/04/07 by Sato, Kohei, Sato, Yusuke
#14B05. 14J17 #14M25 #Algebraic Geometry (math.AG) #FOS: Mathematics

paper · doi:10.48550/arxiv.2004.03522

Abstract

We show a sufficient condition for Fujiki-Oka resolutions of Gorenstein abelian quotient singularities to be crepant in all dimensions by using Ashikaga's continuous fractions. Moreover, we prove that all three dimensional Gorenstein abelian quotient singularities possess a crepant resolution as a corollary. This alternative proof of existence needs only simple computations comparing with the results ever known.

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