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VOL. 74 | 2017 Existence of crepant resolutions
Toshihiro Hayashi, Yukari Ito, Yuhi Sekiya

Editor(s) Keiji Oguiso, Caucher Birkar, Shihoko Ishii, Shigeharu Takayama

Adv. Stud. Pure Math., 2017: 185-202 (2017) DOI: 10.2969/aspm/07410185


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.


Published: 1 January 2017
First available in Project Euclid: 23 October 2018

zbMATH: 1388.14051
MathSciNet: MR3791214

Digital Object Identifier: 10.2969/aspm/07410185

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


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