Abstract
The rank of a symmetric form is the length of its shortest decomposition as a sum of pure powers of linear forms, i.e. the shortest smooth apolar scheme.
The cactus rank of the form is the the length of the shortest apolar scheme.
The a-th cactus variety of cubic forms C_{a,n} is the closure of the family of cubic forms of cactus rank a in the projective space of cubic forms in n+1 variables.
Together with Ranestad I shall report on recent work with Jelisiejew and Marques giving the dimension and a geometric characterization of the general member of C_{a,n}, when 1\leq a\leq 2n+2.