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arXiv · 2211.03708

On the orbits of plane automorphisms and their stabilizers

Iván Pan·Alvaro Rittatore
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Abstract

Let $\Bbbk$ be a perfect field with algebraic closure $\overline{\Bbbk}$. If $H$ is a subgroup of plane automorphisms over $\Bbbk$ and $p\in\overline{\Bbbk}^2$ is a point, we describe the subgroup consisting of plane automorphisms which stabilize the orbit of $p$ under $H$, when this orbit has irreducible closure in $\overline{\Bbbk}^2$. As an application, we treat the case where $H$ is cyclic and the closure of the orbit of $p$ is an arbitrary (non-necessarily irreducible) curve.

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Iván Pan, Alvaro Rittatore. 2022-11-07. On the orbits of plane automorphisms and their stabilizers. https://arxiv.org/abs/2211.03708

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