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Published online by Cambridge University Press: 04 December 2007
Let π : X [xlarr ] Y be a good quotient of a smooth variety X by a reductive algebraic group G and 1[les ]k≤ dim (Y) an integer. We prove that if, locally, any invariant horizontal differential k-form on X (resp. any regular differential k-form on Y) is a Kähler differential form on Y then codim(Ysing)>k+1. We also prove that the dualizing sheaf on Y is the sheaf of invariant horizontal dim(Y)-forms.