Mathematical Research Letters

Volume 18 (2011)

Number 6

Six-dimensional exceptional quotient singularities

Pages: 1121 – 1139



Ivan Cheltsov (University of Edinburgh, Edinburgh EH9 3JZ, U.K.)

Constantin Shramov (Steklov Institute of Mathematics, 8 Gubkina street, Moscow 119991, Russia)


We classify six-dimensional exceptional quotient singularities and show that seven-dimensional exceptional quotient singularities do not exist. Inter alia we prove that the irreducible six-dimensional projective representation of the sporadic simple Hall–Janko group gives rise to an exceptional quotient singularity.

Published 20 February 2012