On subcanonical Gorenstein varieties and apolarity

Let X be a codimension 1 subvariety of dimension greater than 1 of a variety of minimal degree Y. If X is subcanonical with Gorenstein canonical singularities admitting a crepant resolution, then X is arithmetically Gorenstein and we characterize such subvarieties X of Y, via apolarity, as those whose apolar hypersurfaces are Fermat.