Weakly-special threefolds and non-density of rational points

Abstract

We verify part of a conjecture of Campana predicting that rational points on the weakly-special non-special simply-connected smooth projective threefolds constructed by Bogomolov-Tschinkel are not dense. To prove our result, we establish fundamental properties of moduli spaces of orbifold maps, and prove a dimension bound for such moduli spaces by using the recent extension of Kobayashi-Ochiai's finiteness theorem for Campana's orbifold pairs.