Torsion and cotorsion in the sheaf of K\"ahler differentials on some mild singularities

We give a criterion for the sheaf of K\"ahler differentials on a cone over a smooth projective variety to be torsion-free. Applying this to Veronese embeddings of projective space and using known results on differentials on quotient singularities we show that even for mild, e.g. Gorenstein terminal, singularities the sheaf of K\"ahler differentials will in general have torsion and cotorsion.