A characterization of local nilpotence for dimension two polynomial derivations

Abstract

Let $\mathbb{k}$ be an algebraically closed field. We prove that a polynomial $\mathbb{k}$-derivation D in two variables is locally nilpotent if and only if the subgroup of polynomial $\mathbb{k}$-automorphisms which commute with D admits elements whose degree is arbitrary big.

Keywords:

• Locally nilpotent derivations
• polynomials

2020 MATHEMATICS SUBJECT CLASSIFICATION:

• 13N15
• 34A12

Additional information

Funding

Research of I. Pan was partially supported by ANII and PEDECIBA of Uruguay.