We construct a family of fibred threefolds $X_m \to (S , \Delta )$ such that $X_m$ has no étale cover that dominates a variety of general type but it dominates the orbifold $(S,\Delta )$ of general type. Following Campana, the threefolds $X_m$ are called weakly special but not special. The Weak Specialness Conjecture predicts that a weakly special variety defined over a number field has a potentially dense set of rational points. We prove that if m is big enough, the threefolds $X_m$ present behaviours that contradict the function field and analytic analogue of the Weak Specialness Conjecture. We prove our results by adapting the recent method of Ru and Vojta. We also formulate some generalisations of known conjectures on exceptional loci that fit into Campana’s program and prove some cases over function fields.

中文翻译：

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非特殊变种和广义的 Lang-Vojta 猜想

我们构建了一个纤维三折系列 $X_m \to (S , \Delta )$ 这样 $X_m$ 没有主宰各种一般类型的étale封面，但它主宰了orbifold $(S,\Delta )$ 一般类型的。继坎帕纳之后，三重 $X_m$ 被称为弱特殊但不是特别的. 弱特殊性猜想预测，在数域上定义的弱特殊变体具有潜在的密集有理点集。我们证明如果米够大，三折 $X_m$ 存在与弱特殊性猜想的函数场和解析类比相矛盾的行为。我们通过采用最近的 Ru 和 Vojta 方法来证明我们的结果。我们还对适合 Campana 程序的异常轨迹上的已知猜想进行了一些概括，并证明了函数域上的一些案例。