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arXiv · 1708.06221

Density of orbits of dominant regular self-maps of semiabelian varieties

Dragos Ghioca·Matthew Satriano
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Abstract

We prove a conjecture of Medvedev and Scanlon in the case of regular morphisms of semiabelian varieties. That is, if $G$ is a semiabelian variety defined over an algebraically closed field $K$ of characteristic $0$, and $\varphi\colon G\to G$ is a dominant regular self-map of $G$ which is not necessarily a group homomorphism, we prove that one of the following holds: either there exists a non-constant rational fibration preserved by $\varphi$, or there exists a point $x\in G(K)$ whose $\varphi$-orbit is Zariski dense in $G$.

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Dragos Ghioca, Matthew Satriano. 2017-08-21. Density of orbits of dominant regular self-maps of semiabelian varieties. https://arxiv.org/abs/1708.06221

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