Automorphism groups of smooth plane curves

TL;DR

This paper classifies automorphism groups of smooth plane curves of degree at least four, providing bounds, classifications of large groups, and a proof of uniqueness for maximal automorphism groups.

Contribution

It offers a comprehensive classification of automorphism groups of smooth plane curves, including bounds and uniqueness results for maximal automorphism groups.

Findings

Determined the structure of automorphism groups for smooth plane curves of degree ≥ 4.

Provided upper bounds for the order of automorphism groups.

Classified cases with large automorphism groups and proved uniqueness of maximal automorphism groups.

Abstract

The author determines the structure of automorphism groups of smooth plane curves of degree at least four. Furthermore, he gives some upper bounds for the order of automorphism groups of smooth plane curves and classifies the cases with large automorphism groups. This paper also contains a simple proof of the uniqueness of smooth plane curves with the full automorphism group of maximal order for each degree.