On k-rational and k-Du Bois local complete intersections

TL;DR

This paper explores the relationship between k-rational and k-Du Bois singularities in local complete intersections, providing characterizations and vanishing results that deepen understanding of their properties.

Contribution

It proves that k-rational singularities are k-Du Bois in local complete intersections and characterizes k-rationality for hypersurfaces via the minimal exponent.

Findings

k-rational singularities are k-Du Bois in local complete intersections

Characterization of k-rationality in hypersurfaces using minimal exponent

Establishment of local vanishing results for these singularities

Abstract

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].