Fialowski–Penkava's stratification conjecture for moduli spaces of algebras

Let $n$ be a fixed finite dimension, and consider the moduli space of complex Lie or associative algebras of dimension $n$. A jump deformation is a deformation that is equivalent to a different codifferential for every sufficiently small nonzero parameter, while a smooth deformation is a deformation whose nearby codifferentials are pairwise nonequivalent; a smooth deformation factors through a jump deformation when its image is contained in the image of a smooth deformation of the jump's target. Fialowski–Penkava's conjecture. The moduli space of Lie or associative algebras of a fixed finite dimension $n$ are stratified by projective orbifolds, with jump deformations and smooth deformations factoring through jump deformations providing the only deformations between the strata. This conjecture extends the pattern observed in the complex moduli spaces studied by the authors, where strata are connected by jump deformations and are internally described by smooth deformations that do not factor through jumps. The source gives no proof and provides no evidence that the conjecture has been resolved.