Cyclically pure subrings of Du Bois singularities are Du Bois over Q-algebras, with new results even for faithfully flat maps.
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Under a codimension assumption on the singular locus, isomorphism of the m-th differential sheaf implies isomorphisms for all lower i on complex hypersurfaces, with a positive characteristic analogue discussed.
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Pure subrings of Du Bois singularities are Du Bois singularities
Cyclically pure subrings of Du Bois singularities are Du Bois over Q-algebras, with new results even for faithfully flat maps.
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Higher singularities for hypersurfaces
Under a codimension assumption on the singular locus, isomorphism of the m-th differential sheaf implies isomorphisms for all lower i on complex hypersurfaces, with a positive characteristic analogue discussed.