On locally nilpotent derivations of Fermat rings

Abstract

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 \(\mathbb{C}\).