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

Ghioca, Dragos; Satriano, Matthew

doi:10.1090/tran/7475

Density of orbits of dominant regular self-maps of semiabelian varieties
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Trans. Amer. Math. Soc. 371 (2019), 6341-6358 Request permission

Abstract:

We prove a conjecture of Medvedev and Scanlon [Ann. of Math. (2), 179 (2014), no. 1, 81–177] 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 nonconstant 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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