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Article Dans Une Revue Compositio Mathematica Année : 2017

The existence of Zariski dense orbits for polynomial endomorphisms of the affine plane

Résumé

In this paper we prove the following theorem. Let $f:\mathbb{A}^2\rightarrow \mathbb{A}^2$ be a dominate polynomial endomorphisms defined over an algebraically closed field $k$ of characteristic $0$. If there are no nonconstant rational function $g:\mathbb{A}^2-rightarrow \mathbb{P}^1$ satisfying $g\circ f=g$, then there exists a point $p\in \mathbb{A}^2(k)$ whose orbit under $f$ is Zariski dense in $\mathbb{A}^2$. This result gives us a positive answer to a conjecture of Amerik, Bogomolov and Rovinsky ( and Zhang) for polynomial endomorphisms on the affine plane.

Dates et versions

hal-01693854 , version 1 (26-01-2018)

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Junyi Xie. The existence of Zariski dense orbits for polynomial endomorphisms of the affine plane. Compositio Mathematica, 2017, 153 (8), pp.1658-1672. ⟨10.1112/S0010437X17007187⟩. ⟨hal-01693854⟩
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