Injectivity and Vanishing for the Du Bois Complexes of Isolated Singularities

TL;DR

This paper proves an injectivity theorem for Du Bois complexes of varieties with isolated singularities, leading to vanishing results for their higher cohomologies, and extends some results to the non-isolated case and intersection complexes.

Contribution

It introduces an injectivity theorem for Du Bois complexes with isolated singularities and derives new vanishing theorems, extending previous results to broader contexts.

Findings

Proved an injectivity theorem for Du Bois complexes

Derived vanishing theorems for higher Du Bois cohomologies

Extended results to non-isolated singularities and intersection complexes

Abstract

We prove an injectivity theorem for the cohomology of the Du Bois complexes of varieties with isolated singularities. We use this to deduce vanishing statements for the cohomologies of higher Du Bois complexes of such varieties. Besides some extensions and conjectures in the non-isolated case, we also provide analogues for intersection complexes.