On some properties of locally nilpotent derivations

[摘要] 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 SpecB --> SpecA has codimension greater than one in SpecB. Using this result, we give a jacobian formula for certain locally nilpotent derivations of k[X(1),...,X(n)].

[发布日期] 1997-01-30