  As a consequence of our recently established generalized Schmidt's subspace
theorem for closed subschemes in general position, we prove a degeneracy
theorem for integral points on the complement of a union of nef effective
divisors. A novel aspect of our result is the attainment of a strong degeneracy
conclusion (arithmetic quasi-hyperbolicity) under weak positivity assumptions
on the divisors. The proof hinges on applying our recent theorem with a
well-situated ample divisor realizing a certain lexicographical minimax. We
also explore the connections with earlier work by other authors and make a
Conjecture regarding (optimal) bounds for the numbers of divisors necessary,
including consideration of the question of arithmetic hyperbolicity. Under the
standard correspondence between statements in Diophantine approximation and
Nevanlinna theory, one obtains analogous degeneration statements for entire
curves.
