Invariant theory for unipotent groups and an algorithm for computing invariants (Q2766370)

Let \(X = \text{Spec } A\) be an affine variety, \(A\) a \(k\)-algebra and the characteristic of the field \(k\) be arbitrary. Let \(G\) be a unipotent group acting on \(X\). A constructive proof is given for the existence of an open subset \(U \subset X\) such that the geometric quotient (in the sense of Mumford) \(U \to U/G\) exists. In characteristic \(0\) and in case of a proper action, and \(X\) being normal \(U\) turns out to be the maximal open subset of \(X\) on which the geometric quotient exists. As a basis, the case of \(G\) being the additive group is studied in detail. Known results for the case of characteristic \(0\) are extended, respectively generalised to characteristic \(p > 0\).