Non-algebraizable neighborhoods of curves
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arXiv
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| Hauptverfasser: | , , |
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866916338911412224 |
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| author | Luza, Maycol Falla Loray, Frank Sad, Paulo |
| author_facet | Luza, Maycol Falla Loray, Frank Sad, Paulo |
| contents | We provide several families of compact complex curves embedded in smooth complex surfaces such that no neighborhood of the curve can be embedded in an algebraic surface. Different constructions are proposed, by patching neighborhoods of curves in projective surfaces, and blowing down exceptional curves. These constructions generalize examples recently given by S. Lvovski. One of our non algebraic argument is based on an extension theorem of S. Ivashkovich. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2407_20206 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Non-algebraizable neighborhoods of curves Luza, Maycol Falla Loray, Frank Sad, Paulo Algebraic Geometry Complex Variables 51M15, 57N40 We provide several families of compact complex curves embedded in smooth complex surfaces such that no neighborhood of the curve can be embedded in an algebraic surface. Different constructions are proposed, by patching neighborhoods of curves in projective surfaces, and blowing down exceptional curves. These constructions generalize examples recently given by S. Lvovski. One of our non algebraic argument is based on an extension theorem of S. Ivashkovich. |
| title | Non-algebraizable neighborhoods of curves |
| topic | Algebraic Geometry Complex Variables 51M15, 57N40 |
| url | https://arxiv.org/abs/2407.20206 |