Stable symmetries of plane sextics

TL;DR

This paper classifies stable projective symmetries of irreducible plane sextic curves with simple singularities and explores their connection to maximal trigonal curves.

Contribution

It provides a classification of stable symmetries of plane sextics and links order 2 symmetries to maximal trigonal curves.

Findings

Classification of stable symmetries for plane sextics.

Connection established between order 2 symmetries and maximal trigonal curves.

Framework for understanding symmetries under equivariant deformations.

Abstract

We classify projective symmetries of irreducible plane sextics with simple singularities which are stable under equivariant deformations. We also outline a connection between order~2 stable symmetries and maximal trigonal curves.