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

TL;DR

This paper proves a key theorem related to Vojta's abc conjecture and explores specific cases of Campana's orbifold conjecture, providing new insights into complex analytic mappings and their intersection properties.

Contribution

It introduces a truncated second main theorem with explicit exceptional sets for analytic maps into projective plane, advancing understanding of orbifold conjectures.

Findings

Established a second main theorem with explicit bounds

Analyzed cases of Campana's orbifold conjecture for specific covers

Provided new results on intersection multiplicities in complex geometry

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.