We generalize to arbitrary dimension our previous construction of simply connected weakly-special but not special varieties. We show that they satisfy the function field and complex analytic part of Campana's conjecture. Moreover, we give examples, in any dimension, of smooth simply connected nonisotrivial projective varieties of general type that satisfy the function field Lang and Vojta conjectures with an explicit exceptional set.
Lu et al. (Wed,) studied this question.