# An Automorphic Classification of Real Cubic Curves

## TL;DR

This paper classifies real cubic curves by analyzing the action of ring automorphisms on degree-three polynomials, identifying orbit representatives to understand their equivalence classes.

## Contribution

It provides an automorphic classification of real cubic curves, detailing the orbit structure under polynomial ring automorphisms.

## Key findings

- Computed the orbits of degree-three polynomials under automorphisms
- Identified a representative for each orbit of real cubic curves
- Enhanced understanding of the symmetry and classification of real cubic curves

## Abstract

The action of ring automorphisms of the polynomial ring in two variables over the real numbers on real plane curves is considered. The orbits containing degree-three polynomials are computed, with one representative per orbit being selected.