Hodge filtration on local cohomology, Du Bois complex, and local cohomological dimension

TL;DR

This paper investigates the Hodge filtration on local cohomology sheaves of smooth complex varieties along a subscheme, linking it to log resolutions and deriving applications for cohomological dimension, Du Bois complex, and vanishing results.

Contribution

It introduces a new approach to understanding the Hodge filtration on local cohomology using log resolutions, with novel applications to several geometric and cohomological properties.

Findings

Established connections between Hodge filtration and local cohomological dimension.

Derived new vanishing theorems related to the Du Bois complex.

Provided insights into reflexive differentials associated to subschemes.

Abstract

We study the Hodge filtration on the local cohomology sheaves of a smooth complex algebraic variety along a closed subscheme Z in terms of log resolutions, and derive applications regarding the local cohomological dimension, the Du Bois complex, local vanishing, and reflexive differentials associated to Z.