Computing quotients by connected solvable groups. (March 2022) - Kemper, Gregor
Abstract: Consider an action of a connected solvable group G on an affine variety X . This paper presents an algorithm that constructs a semi-invariant f ∈ K [ X ] = : R and computes the invariant ring ( R f ) G together with a presentation. The morphism X f → Spec ( ( R f ) G ) obtained from the algorithm is a universal geometric quotient. In fact, it is even better than that: a so-called excellent quotient. If R is a polynomial ring, the algorithm requires no Gröbner basis computations. If R is a complete intersection, then so is ( R f ) G .