# On toric face rings I

## TL;DR

This paper constructs an explicit Deligne-Du Bois complex for algebraic varieties locally isomorphic to toric face rings, advancing understanding of their singularities and cohomological properties.

## Contribution

It introduces a novel explicit construction of the Deligne-Du Bois complex for a class of algebraic varieties related to toric face rings.

## Key findings

- Explicit Deligne-Du Bois complex constructed for these varieties
- Enhanced understanding of their singularity structure
- Potential applications to cohomological studies

## Abstract

We construct an explicit Deligne - Du Bois complex for algebraic varieties which are locally analytically isomorphic to the spectrum of a toric face ring.