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As a consequence of our recently established generalized Schmidt's subspacetheorem for closed subschemes in general position, we prove a degeneracytheorem for integral points on the complement of a union of nef effectivedivisors. A novel aspect of our result is the attainment of a strong degeneracyconclusion (arithmetic quasi-hyperbolicity) under weak positivity assumptionson the divisors. The proof hinges on applying our recent theorem with awell-situated ample divisor realizing a certain lexicographical minimax. Wealso explore the connections with earlier work by other authors and make aConjecture regarding (optimal) bounds for the numbers of divisors necessary,including consideration of the question of arithmetic hyperbolicity. Under thestandard correspondence between statements in Diophantine approximation andNevanlinna theory, one obtains analogous degeneration statements for entirecurves.

On the degeneracy of integral points and entire curves in the complement of nef effective divisors