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Cases of Campana's orbifold conjecture and Vojta's general abc conjecture for orbifold entire curves

Abstract

We study Campana’s orbifold conjecture for finite ramified covers of P2 with three components admitting sufficiently large multiplicities. We also prove a truncated second main theorem of level one for analytic maps into P2 intersecting the coordinate lines in sufficiently high multiplicities. In particular, the exceptional set for the later result can be described explicitly.

This is joint work with Ji Guo.