Simply connectedness and hyperbolicity

TL;DR

This paper constructs new examples of simply connected varieties that satisfy important conjectures in algebraic geometry, extending previous work and providing the first such examples in higher dimensions.

Contribution

It generalizes previous constructions to arbitrary dimensions and provides the first examples of simply connected, nonisotrivial, general type varieties satisfying Lang's conjecture.

Findings

Constructed simply connected weakly-special but not special varieties in arbitrary dimensions.

Showed these varieties satisfy Campana's conjecture in function field and complex analytic forms.

Provided the first examples of smooth simply connected nonisotrivial projective varieties of general type satisfying Lang's conjecture.

Abstract

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 the first examples, in any dimension, of smooth simply connected nonisotrivial projective varieties of general type that satisfy the function field Lang's conjecture.