A complex case of Vojta's general abc conjecture and cases of Campana's orbifold conjecture

Abstract

We proved a truncated second main theorem of level one with explicit exceptional sets for analytic maps into $\mathbb P^2$ intersecting the coordinate lines with sufficiently high multiplicities. As applications, we studied some cases of Campana's orbifold conjecture for $\mathbb P^2$ and finite ramified covers of $\mathbb P^2$ with three components admitting sufficiently large multiplicities.