4 problems

Let $(X, \Delta)$ be a smooth C-pair over $\overline{\mathbb{Q}}$. Say that $(X, \Delta)$ satisfies potential density of integral points if, for some number field $K$, finite set o…

Let $(X, \Delta)$ be a smooth C-pair over $\mathbb{C}$, where a dense entire curve means a holomorphic C-pair map $\mathbb{C} \to (X, \Delta)^{\an}$ whose image is Zariski-dense in…

Let $(X,D)$ be a C-pair, meaning a pair consisting of a complex space $X$ and a boundary divisor $D$ with Campana's orbifold multiplicities, and suppose that $X$ is compact Kähler.…

Let $(X,D)$) be a log canonical C-pair, where $X$ is compact Kähler. The augmented irregularity of the pair is denoted by $q^+(X,D)$. Campana's augmented irregularity conjecture. I…