Classification of toric surface singularities

TL;DR

This paper provides a classification of two-dimensional toric surface singularities based on their minimal log discrepancy, offering a systematic understanding of these mathematical objects.

Contribution

It introduces a classification scheme for toric surface singularities using minimal log discrepancy, a novel approach in this context.

Findings

Complete classification of 2D toric surface singularities

Identification of minimal log discrepancy as a key invariant

Framework for analyzing singularities in algebraic geometry

Abstract

We classify two-dimensional toric log germs in terms of their minimal log discrepancy.