On some properties of locally nilpotent derivations Original Research Article

Let k be a field of characteristic zero, and let B be a k-domain. We characterize, among all subalgebras A of B, those which are kernels of locally nilpotent derivations D: B → B. If A is such a ring, and if we assume that B is a UFD and that both A and B are finitely generated over k, then we show that the set of nonsmooth points of the morphism Spec B → Spec A has codimension greater than one in Spec B. Using this result, we give a jacobian formula for certain locally nilpotent derivations of k[X1, …, Xn].