Abstract
We classify six-dimensional exceptional quotient singularities and show that seven- dimensional exceptional quotient singularities do not exist. Inter alia we prove that the irre- ducible six-dimensional projective representation of the sporadic simple Hall-Janko group gives rise to an exceptional quotient singularity. where Ei is a ξ-exceptional divisor, and bi ∈ Q. Let B be an effective Q-divisor on V. Put B = m X i=1 aiBi, where Bi is a prime Weil divisor on V , and ai ∈ Q>0. Suppose that B is a Q-Cartier divisor. Then m X i=1 ai ¯ Bi ∼Q ξ ∗ m X i=1 aiBi !
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