Steenbrink vanishing extended

Abstract

The notion of DB index, a measure of how far a singularity of a pair is from being Du Bois, is introduced and used to generalize vanishing theorems of Steenbrink and others with simpler and more natural proofs than the originals.Comment: To appear in the Proceedings of 12th ALGA meeting dedicated to Aron Simis and Steven Kleiman (Bulletin of the Brazilian Mathematical Society). Some typos are corrected in v2, but no essential change from v