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arXiv · 2408.14061

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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Serge Lvovski. 2024-08-26. On fields of meromorphic functions on neighborhoods of rational curves. https://arxiv.org/abs/2408.14061

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