On locally nilpotent derivations of Fermat rings

Let $B_n^m =\frac{\mathbb{C}[X_1,\ldots, X_n]}{(X_1^m+\cdots +X_n^m)}$ (Fermat ring), where $m\geq2$ and $n\geq3$. In a recent paper D. Fiston and S. Maubach show that for $m\geq n^2-2n$ the unique locally nilpotent derivation of $B_n^m$ is the zero derivation. In this note we prove that the ring $B_n^2$ has non-zero irreducible locally nilpotent derivations, which are explicitly presented, and that its ML-invariant is $\mathbb{C}$.