Vojta's abc conjecture for entire curves in toric varieties highly ramified over the boundary

Abstract

We prove Vojta's abc conjecture for projective space ${\mathbb{P}}^n(\mathbb{C})$, assuming that the entire curves in ${\mathbb{P}}^n(\mathbb{C})$ are highly ramified over the coordinate hyperplanes. This extends the results of Guo Ji and the second-named author for the case $n=2$ (see \cite{GW22}). We also explore the corresponding results for projective toric varieties. Consequently, we establish a version of Campana's orbifold conjecture for finite coverings of projective toric varieties.