The minimal exponent of a reduced hypersurface is characterized by vanishing and isomorphism conditions on higher direct images of twisted logarithmic differential forms on a log resolution.
On k-rational and k-Du Bois local complete intersections
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We show that k-rational singularities of local complete intersections are k-Du Bois. For hypersurfaces, we characterize k-rationality in terms of the minimal exponent. We also establish some local vanishing results for k-rational and k-Du Bois singularities. Some of these results have been independently obtained in [FL2].
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A birational description of the minimal exponent
The minimal exponent of a reduced hypersurface is characterized by vanishing and isomorphism conditions on higher direct images of twisted logarithmic differential forms on a log resolution.