Higher Du Bois and Higher Rational Pairs

Abstract

We extend the notions of higher Du Bois and higher rational singularities to pairs in the sense of the minimal model program. We extend numerous results to these higher pairs, including Bertini type theorems, stability under finite maps and that m-rational pairs are m-Du Bois. We prove these using a generalized Kovács-Schwede-type injectivity theorem for pairs, the main technical result of this paper.