DB pairs and vanishing theorems

TL;DR

This paper introduces DuBois singularities for pairs and proves a vanishing theorem, extending to resolutions of log canonical singularities, advancing the understanding of singularity theory in algebraic geometry.

Contribution

It defines DuBois singularities for pairs and establishes a new vanishing theorem, broadening the scope of singularity and vanishing results in algebraic geometry.

Findings

Defined DuBois singularities for pairs

Proved a new vanishing theorem for these singularities

Extended results to resolutions of log canonical singularities

Abstract

The main purpose of this article is to define the notion of DuBois singularities for pairs and proving a vanishing theorem using this new notion. The main vanishing theorem specializes to a new vanishing theorem for resolutions of log canonial singularities.