# On toric face rings II

## TL;DR

This paper introduces weakly log canonical singularities, generalizes semi-log canonical singularities, and classifies toric varieties with these singularities, including residue analysis for lc centers.

## Contribution

It defines weakly log canonical singularities and classifies associated toric varieties, extending the understanding of singularities in algebraic geometry.

## Key findings

- Classification of toric varieties with weakly log canonical singularities
- Introduction of weakly log canonical singularities as a generalization
- Residue analysis for lc centers of various codimensions

## Abstract

We introduce the class of weakly log canonical singularities, a natural generalization of semi-log canonical singularities. Toric varieties (associated to toric face rings, possibly non-normal or reducible) which have weakly (semi-) log canonical singularities are classified. In the toric case, we discuss residues to lc centers of codimension one or higher.