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.