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## Weakly-exceptional singularities in higher dimensions

Journal fuer die reine und angewandte Mathematik. 2014. Vol. 689. P. 201-241.

We show that infinitely many Gorenstein weakly-exceptional quotient singularities exist in all dimensions, we prove a weak-exceptionality criterion for five-dimensional quotient singularities, and we find a sufficient condition for being weakly-exceptional for six-dimensional quotient singularities. The proof is naturally linked to various classical geometrical constructions related to subvarieties of small degree in projective spaces, in particular Bordiga surfaces and Bordiga threefolds.