# Gorenstein graphic matroids

## TL;DR

This paper characterizes when the toric variety of a graphic matroid is Gorenstein, providing a complete graph-theoretic classification based on matroid properties.

## Contribution

It offers the first complete classification of Gorenstein toric varieties arising from graphic matroids using graph-theoretic criteria.

## Key findings

- Identifies graph conditions for Gorenstein property
- Classifies all graphic matroids with Gorenstein toric varieties
- Connects matroid theory with algebraic geometry

## Abstract

The toric variety of a matroid is projectively normal, and therefore it is Cohen-Macaulay. We provide a complete graph-theoretic classification when the toric variety of a graphic matroid is Gorenstein.