Flexible bundles over rigid affine surfaces

Abstract

We construct a smooth rational affine surface $S$ with finite automorphism group but with the property that the group of automorphisms of the cylinder $S\times {\mathbb{A}}^2$ acts infinitely transitively on the complement of a closed subset of codimension at least two. Such a surface $S$ is in particular rigid but not stably rigid with respect to the Makar–Limanov invariant.