# Equivariant Degenerations of Plane Curve Orbits

## TL;DR

This paper studies how plane curve orbits, especially quartics, degenerate under natural specializations, extending previous work on orbit degrees to an equivariant setting.

## Contribution

It generalizes the computation of orbit degrees to the equivariant setting, providing a detailed analysis for plane quartic curves.

## Key findings

- Complete picture of orbit degenerations for plane quartics
- Extension of degree computations to equivariant setting
- Insights into orbit structure under degenerations

## Abstract

In a series of papers, Aluffi and Faber computed the degree of the $GL_3$ orbit closure of an arbitrary plane curve. We attempt to generalize this to the equivariant setting by studying how orbits degenerate under some natural specializations, yielding a fairly complete picture in the case of plane quartics.