On the conjectures of Vojta and Campana over function fields with explicit exceptional sets

Abstract

We prove new cases of Vojta's conjectures for surfaces in the context of function fields, with truncation equal to one and providing an effective explicit description of the exceptional set. We also prove a general and explicit result towards Campana's conjecture over complex function fields of curves. Our methods rely on a local study of $\omega$-integral varieties.