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arXiv · 2010.16291

The Geometric Dynamical Northcott Property For Regular Polynomial Automorphisms of the Affine Plane

Thomas Gauthier·Gabriel Vigny
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Abstract

We establish the finiteness of periodic points, that we called Geometric Dynamical Northcott Property, for regular polynomials automorphisms of the affine plane over a function field $\mathbf{K}$ of characteristic zero, improving results of Ingram. For that, we show that when $\mathbf{K}$ is the field of rational functions of a smooth complex projective curve, the canonical height of a subvariety is the mass of an appropriate bifurcation current and that a marked point is stable if and only if its canonical height is zero. We then establish the Geometric Dynamical Northcott Property using a similarity argument.

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BibTeXRIS

Thomas Gauthier, Gabriel Vigny. 2020-10-30. The Geometric Dynamical Northcott Property For Regular Polynomial Automorphisms of the Affine Plane. https://arxiv.org/abs/2010.16291

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