On the orbits of plane automorphisms and their stabilizers

2022/11/07 by Iván Pan, Pan, Iván, Alvaro Rittatore +1 · 1 citation
Mathematics · #14R10 #14R20 #Advanced Algebra and Geometry #Advanced Differential Equations and Dynamical Systems #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics

paper · pdf · doi:10.48550/arxiv.2211.03708

openalex publication_date 2022/11/07 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let \Bbbk be a perfect field with algebraic closure \Bbbk. If H is a subgroup of plane automorphisms over \Bbbk and p∈\Bbbk² 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 \Bbbk². 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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