On fields of meromorphic functions on neighborhoods of rational curves
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arXiv
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866917903884877824 |
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| author | Lvovski, Serge |
| author_facet | Lvovski, Serge |
| contents | 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 $\mathbb C$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2408_14061 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On fields of meromorphic functions on neighborhoods of rational curves Lvovski, Serge Complex Variables Algebraic Geometry 32H99, 32G13 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 $\mathbb C$. |
| title | On fields of meromorphic functions on neighborhoods of rational curves |
| topic | Complex Variables Algebraic Geometry 32H99, 32G13 |
| url | https://arxiv.org/abs/2408.14061 |