Nonspecial varieties and generalised Lang–Vojta conjectures

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