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arXiv · 1604.04933

On plane polynomial automorphisms commuting with simple derivations

Luís Gustavo Mendes·Ivan Pan
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Abstract

We consider the subgroup Aut(D) consisting of automorphisms of K[x,y] commuting with a derivation D, where K is an algebraically closed field of characteristic 0. We prove that if D is simple (i.e. D does not stabilize non-trivial ideals), then Aut(D)=1, in the case where D is of Shamsuddin type this result was proven by R.Baltazar in 2014 (arXiv:1412.8373). Moreover, we describe Aut(D) for Shamsuddin type derivations and deduce that Aut(D)=1 for a general such derivation implies D is simple.

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Luís Gustavo Mendes, Ivan Pan. 2016-04-17. On plane polynomial automorphisms commuting with simple derivations. https://arxiv.org/abs/1604.04933

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