## Advanced Studies in Pure Mathematics

### Existence of crepant resolutions

#### 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.

#### Article information

Dates
Revised: 22 October 2013
First available in Project Euclid: 23 October 2018

https://projecteuclid.org/ euclid.aspm/1540319488

Digital Object Identifier
doi:10.2969/aspm/07410185

Mathematical Reviews number (MathSciNet)
MR3791214

Zentralblatt MATH identifier
1388.14051

#### Citation

Hayashi, Toshihiro; Ito, Yukari; Sekiya, Yuhi. Existence of crepant resolutions. Higher Dimensional Algebraic Geometry: In honour of Professor Yujiro Kawamata's sixtieth birthday, 185--202, Mathematical Society of Japan, Tokyo, Japan, 2017. doi:10.2969/aspm/07410185. https://projecteuclid.org/euclid.aspm/1540319488