On fields of meromorphic functions on neighborhoods of rational curves

Serge Lvovski
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Abstract

Suppose that $F$ is a smooth and connected complex surface (not necessarily compact) containing a smooth rational curve with positive self-intersection. We prove that if there exists a non-constant meromorphic function on $F$, then the field of meromorphic functions on $F$ is isomorphic to the field of rational functions in one or two variables over $\mathbb C$.
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论有理曲线邻域上的分形函数场
假设 $F$ 是一个光滑连通的复曲面(不一定紧凑),包含一条光滑有理曲线,其自交为正。我们证明,如果 $F$ 上存在一个非恒定的分形函数,那么 $F$ 上的分形函数域与 $mathbb C$ 上的一或二变量有理函数域同构。
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