  For real and complex homogeneous cubic polyomials in $n+1$ variables, we
prove that the Chow variety of products of linear forms is generically complex
identifiable for all ranks up to the generic rank minus two. By integrating
fundamental results of [Oeding, Hyperdeterminants of polynomials, Adv. Math.,
2012], [Casarotti and Mella, From non defectivity to identifiability, J. Eur.
Math. Soc., 2021], and [Torrance and Vannieuwenhoven, All secant varieties of
the Chow variety are nondefective for cubics and quaternary forms, Trans. Amer.
Math. Soc., 2021] the proof is reduced to only those cases in up to $103$
variables. These remaining cases are proved using the Hessian criterion for
tangential weak defectivity from [Chiantini, Ottaviani, and Vannieuwenhoven, An
algorithm for generic and low-rank specific identifiability of complex tensors,
SIAM J. Matrix Anal. Appl., 2014]. We also establish that the smooth loci of
the real and complex Chow varieties are immersed minimal submanifolds in their
usual ambient spaces.
