Abstract
Let $G$ be a finite subgroup of $\operatorname{SL}(n,\mathbb{C})$, then the quotient $\mathbb{C}^n/G$ has a Gorenstein canonical singularity. If $n=2\ \text{or}\ 3$, it is known that there exist crepant resolutions of the quotient singularity. In higher dimension, there are many results which assume existence of crepant resolutions. However, few examples of crepant resolutions are known. In this paper, we will show several trials to obtain crepant resolutions and give a conjecture on existence of crepant resolutions.
Information
Published: 1 January 2017
First available in Project Euclid: 23 October 2018
zbMATH: 1388.14051
MathSciNet: MR3791214
Digital Object Identifier: 10.2969/aspm/07410185
Subjects:
Primary:
13P10
,
14C05
,
14L30
Secondary:
14E15
,
14M25
Keywords:
Crepant reosltuion
,
Grobner basis
,
Hilbert scheme
,
McKay correspondence
,
quotient singularity
,
toric variety
Rights: Copyright © 2017 Mathematical Society of Japan
