From the text: The main results in the authors’ paper [ibid. 50, 291–297 (2013; Zbl 1258.14063)] concern minimal length apolar subschemes to cubic forms. Apolarity is defined via an action on polynomials by a dual polynomial ring. In the paper the action is defined as differentiation: \(T := \mathbb{C}[y_0,\dots, y_n]\) acting on \(S = \mathbb{C}[x_0,\dots, x_n]\) by \[ y_i(x_i)=\frac{d}{dx_j}(x_i)=\delta_{ij}. \] Which means that \(y^2_j (x^2_i) = 2\delta_{ij}\). Alternatively one may define the action by contraction, which means that \(y^2_j (x^2_i) = \delta_{ij}\). With the action defined by differentiation, the proof of Lemma 2 is incorrect, however with the action defined by contraction, the proof is correct. Differentiation should therefore be substituted by contraction in the paper, since this lemma is used throughout.