On the classification of toric singularities

TL;DR

This paper investigates the relationship between minimal log discrepancy and Cartier index in toric log varieties, providing bounds that enhance understanding of their local singularity structure.

Contribution

It establishes a bound on the Cartier index based on minimal log discrepancy for toric log varieties with standard coefficients.

Findings

Minimal log discrepancy bounds the Cartier index at invariant points.

Provides new insights into the local structure of toric singularities.

Enhances classification methods for toric singularities.

Abstract

For a toric log variety with standard coefficients, we show that the minimal log discrepancy at a closed invariant point bounds the Cartier index of a neighbourhood.