A dynamical characterisation of smooth cubic affine surfaces of Markov type
Algebraic Geometry
2025-12-12 v1 Complex Variables
Dynamical Systems
Abstract
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.
Keywords
Cite
@article{arxiv.2512.10455,
title = {A dynamical characterisation of smooth cubic affine surfaces of Markov type},
author = {Marc Abboud},
journal= {arXiv preprint arXiv:2512.10455},
year = {2025}
}