Motivated by the notion of the algebraic hyperbolicity, we introduce the notion of Nevanlinna hyperbolicity for a pair (X,D), where X is a projective variety and D is an effective Cartier divisor on X. This notion links and unifies the Nevanlinna theory, the complex hyperbolicity (Brody and Kobayashi hyperbolicity), the big Picard-type extension theorem (more generally the Borel hyperbolicity). It also implies the algebraic hyperbolicity. The key is to use the Nevanlinna theory on parabolic Riemann surfaces recently developed by Păun and Sibony [Value distribution theory for parabolic Riemann surfaces, preprint (2014), arXiv:1403.6596].

中文翻译：

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Nevanlinna 和代数双曲线

受代数双曲概念的启发，我们引入了内万林纳双曲对于一对(X,D)， 在哪里X是一个射影变体并且D是一个有效的卡地亚除数X. 这个概念连接并统一了 Nevanlinna 理论、复双曲线（Brody 和 Kobayashi 双曲线）、大 Picard 型扩展定理（更普遍地是 Borel 双曲线）。它还暗示了代数双曲性。关键是利用 P 最近开发的抛物线黎曼曲面上的 Nevanlinna 理论一种un 和 Sibony [抛物线黎曼曲面的价值分布理论，预印本 (2014)，arXiv:1403.6596]。