Weakly-special threefolds and non-density of rational points

TL;DR

This paper investigates the distribution of rational points on certain threefolds, confirming a conjecture that such points are not dense, by analyzing moduli spaces of orbifold maps and applying advanced finiteness theorems.

Contribution

It establishes fundamental properties of orbifold moduli spaces and proves a dimension bound using recent finiteness results, advancing understanding of rational points on weakly-special threefolds.

Findings

Rational points are not dense on the studied threefolds.

Fundamental properties of orbifold moduli spaces are established.

A dimension bound for moduli spaces is proved using recent theorems.

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.