We prove the existence of (non compact) complex surfaces with a smooth rational curve embedded such that there does not exist any formal singular foliation along the curve. In particular, at arbitrary small neighborhood of the curve, any meromorphic function is constant. This implies that the Picard group is not countably generated.

中文翻译：

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没有函数的有理曲线的邻域

我们证明了（非紧致）复杂表面的存在，该表面嵌入了平滑的有理曲线，因此沿曲线不存在任何形式的奇异叶。特别是，在曲线的任意小邻域中，任何亚纯函数都是恒定的。这意味着无法生成Picard组。