A dynamical characterisation of smooth cubic affine surfaces of Markov type

Fuente: arXiv
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Autore principale: Abboud, Marc
Natura: Preprint
Pubblicazione: 2025
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author Abboud, Marc
author_facet Abboud, Marc
contents Using valuative techniques, we show that a smooth affine surface with a non-elementary automorphism group and completable by a cycle of rational curves is either the algebraic torus or a smooth cubic affine surface of Markov type. Furthermore we show that smooth cubic affine surfaces of Markov type do no admit dominant endomorphisms which are not automorphisms.
format Preprint
id arxiv_https___arxiv_org_abs_2512_10455
institution arXiv
publishDate 2025
record_format arxiv
spellingShingle A dynamical characterisation of smooth cubic affine surfaces of Markov type
Abboud, Marc
Algebraic Geometry
Complex Variables
Dynamical Systems
37F10, 37F80, 13A18, 37P99
Using valuative techniques, we show that a smooth affine surface with a non-elementary automorphism group and completable by a cycle of rational curves is either the algebraic torus or a smooth cubic affine surface of Markov type. Furthermore we show that smooth cubic affine surfaces of Markov type do no admit dominant endomorphisms which are not automorphisms.
title A dynamical characterisation of smooth cubic affine surfaces of Markov type
topic Algebraic Geometry
Complex Variables
Dynamical Systems
37F10, 37F80, 13A18, 37P99
url https://arxiv.org/abs/2512.10455