Equivariant Degenerations of Plane Curve Orbits

Abstract

In a series of papers, Aluffi and Faber computed the degree of the $G{L}_3$ 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.

arXiv comment51 pages, revised following referee report, accepted to Transactions of the American Mathematical Society