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

2017/08/21 by Ghioca, Dragos, Satriano, Matthew
#Algebraic Geometry (math.AG) #FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.1708.06221

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 φ\colon G→ 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 φ, or there exists a point x∈ G(K) whose φ-orbit is Zariski dense in G.

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