Automorphisms of affine Veronese surfaces

Abstract

We prove that every derivation and every locally nilpotent derivation of the subalgebra [Formula: see text], where [Formula: see text], of the polynomial algebra [Formula: see text] in two variables over a field [Formula: see text] of characteristic zero is induced by a derivation and a locally nilpotent derivation of [Formula: see text], respectively. Moreover, we prove that every automorphism of [Formula: see text] over an algebraically closed field [Formula: see text] of characteristic zero is induced by an automorphism of [Formula: see text]. We also show that the group of automorphisms of [Formula: see text] admits an amalgamated free product structure.