The intuitive definition of Du Bois singularities

TL;DR

This paper establishes an equivalence between Du Bois singularities on projective varieties and a specific condition relating their coherent cohomology groups to Hodge components of singular cohomology, deepening understanding of their geometric properties.

Contribution

It provides a new characterization of Du Bois singularities in terms of cohomological conditions, linking algebraic and Hodge-theoretic perspectives.

Findings

Du Bois singularities are characterized by cohomological conditions.

The equivalence connects algebraic and Hodge-theoretic descriptions.

This result advances the understanding of singularities in algebraic geometry.

Abstract

It is proved that for projective varieties having Du Bois singularities is equivalent to the condition that the coherent cohomology groups of the structure sheaf coincide with the appropriate Hodge components of the singular cohomology groups.