We define and study jet bundles in the geometric orbifold category. We show that the usual arguments from the compact and the logarithmic settings do not all extend to this more general framework. This is illustrated by simple examples of orbifold pairs of general type that do not admit any global jet differential, even if some of these examples satisfy the Green-Griffiths-Lang conjecture. This contrasts with an important result of Demailly (2010) proving that compact varieties of general type always admit jet differentials. We illustrate the usefulness of the study of orbifold jets by establishing the hyperbolicity of some orbifold surfaces, that cannot be derived from the current techniques in Nevanlinna's theory. We also conjecture that Demailly's theorem should hold for orbifold pairs with smooth boundary divisors under a certain natural multiplicity condition, and provide some evidence towards it.

中文翻译：

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轨道双曲线

我们定义和研究几何轨道类别中的射流丛。我们表明来自紧凑和对数设置的常用参数并不都扩展到这个更通用的框架。这可以通过一般类型的轨道对的简单例子来说明，这些例子不承认任何全球喷流差异，即使其中一些例子满足格林-格里菲思-朗猜想。这与 Demailly (2010) 的一个重要结果形成对比，该结果证明一般类型的紧凑变体总是允许射流差异。我们通过建立一些无法从 Nevanlinna 理论中的当前技术推导出的双曲曲面来说明轨道喷流研究的有用性。我们还推测 Demailly'