Stabilization of fields of meromorphic functions on neighborhoods of a rational curve
Fuente:
arXiv
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| Autore principale: | |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| Accesso online: | |
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| _version_ | 1866918025209315328 |
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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 $C$ 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 $U$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2505_13045 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Stabilization of fields of meromorphic functions on neighborhoods of a rational curve Lvovski, Serge Complex Variables Algebraic Geometry 32H99, 14E07 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 $U$. |
| title | Stabilization of fields of meromorphic functions on neighborhoods of a rational curve |
| topic | Complex Variables Algebraic Geometry 32H99, 14E07 |
| url | https://arxiv.org/abs/2505.13045 |