On automorphisms of Danielewski surfaces

Abstract

We develop techniques for computing the AK invariant of a domain with arbitrary characteristic. We use these techniques to describe for any field $K$ the automorphism group of $K[X,Y,Z]/(X^{n}Y-Z^2-h(X)Z)$, where $h(0)\ne 0$ and $n\ge 2$, as well as the isomorphism classes of these algebras.