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.

中文翻译：

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关于nef有效因数的补中积分点和整曲线的退化

由于我们最近建立的广义施密特子空间定理用于一般位置的封闭子方案，我们证明了 nef 有效因数的并集上的积分点的简并定理。我们结果的一个新颖方面是在对除数的弱正假设下获得了强退化结论（算术准双曲性）。证明取决于将我们最近的定理应用到一个位置合适的充分除数来实现某个字典序极小极大值。我们还探索了与其他作者早期工作的联系，并对必要的除数数量的（最佳）边界进行了猜想，包括考虑算术双曲线问题。在丢番图近似中的陈述与涅万林纳理论之间的标准对应关系下，