The paper proves that orbifold entire curves on projective varieties with numerically parallel boundary divisors and sufficiently high multiplicity must be algebraically degenerate, a new case of Campana's orbifold conjecture.
Laurent, ´Equations diophantiennes exponentielles , Invent
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Campana's orbifold conjecture for numerically equivalent divisors
The paper proves that orbifold entire curves on projective varieties with numerically parallel boundary divisors and sufficiently high multiplicity must be algebraically degenerate, a new case of Campana's orbifold conjecture.