Title: Density of orbits of dominant regular self-maps of semiabelian varieties,
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
$G$.