On conjugacy of additive actions in the affine Cremona group

Abstract

An additive action on an irreducible algebraic variety X is an effective action Gn/a  × X → X with an open orbit of the vector group Gn/a. Any two additive actions on X are conjugate by a birational automorphism of X. We prove that, if X is the projective space, the conjugating element can be chosen in the affine Cremona group and it is given by so-called basic polynomials of the corresponding local algebra.