Abstract
We describe the set of all locally nilpotent derivations of the quotient ring K[X,Y,Z]/(f(X)Y−φ(X,Z)) constructed from the defining equation f(X)Y=φ(X,Z) of a generalized Danielewski surface in K3 for a specific choice of polynomials f and φ, with K an algebraically closed field of characteristic zero. As a consequence of this description we calculate the ML-invariant and the Derksen invariant of this ring. We also determine a set of generators for the group of K-automorphisms of K[X,Y,Z]/(f(X)Y−φ(Z)) also for a specific choice of polynomials f and φ.
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