Abstract

The notion of DB index, a measure of how far a singularity of a pair is frombeingDu Bois, is introduced and used to generalize vanishing theorems of [Ste85], [GKKP11], and [Kov11] with simpler and more natural proofs than the originals. An argument used in one of these proofs also yields an additional theorem connecting various push forwards that lie outside of the range of the validity of the above vanishing theorems.

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