Mathematics > Complex Variables
[Submitted on 19 May 2025
]
Title: Stabilization of fields of meromorphic functions on neighborhoods of a rational curve
Title: 可理曲线邻域上亚纯函数场的稳定化
Abstract: Suppose that $F$ is a smooth and connected complex surface (not necessarily compact) containing a smooth rational curve $C$ with positive self-intersection. We prove that there exists a neighborhood $U\supset C$ such that any meromorphic function defined on a connected neighborhood of $C$ in $U$ can be extended to a meromorphic function on the entire $U$.
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