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arXiv · 2512.10455

A dynamical characterisation of smooth cubic affine surfaces of Markov type

Marc Abboud
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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.

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Marc Abboud. 2025-12-11. A dynamical characterisation of smooth cubic affine surfaces of Markov type. https://arxiv.org/abs/2512.10455

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