Cubic forms in three variables are parametrised by points of a projective space $\P^9$. We study the subvarieties in this space defined by decomposable forms. Specifically, we calculate their equivariant minimal resolutions and describe their ideals invariant-theoretically.
"Decomposable Ternary Cubics." Experiment. Math. 11 (1) 69 - 80, 2002.