Pencils of plane cubics with one base point
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arXiv
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| Auteurs principaux: | , , |
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866911086223032320 |
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| author | Moschetti, Riccardo Pirola, Gian Pietro Stoppino, Lidia |
| author_facet | Moschetti, Riccardo Pirola, Gian Pietro Stoppino, Lidia |
| contents | We study pencils of plane cubics with only one base point and general member smooth, giving a complete classification. Under the additional hypothesis that all members are irreducible, we prove that there exists a unique non-isotrivial pencil with these properties up to projective transformation. We compare our construction with the classical approaches given by Gattazzo, Beauville and Miranda-Persson. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2407_04569 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Pencils of plane cubics with one base point Moschetti, Riccardo Pirola, Gian Pietro Stoppino, Lidia Algebraic Geometry 14C21, 14H50, 14H10 We study pencils of plane cubics with only one base point and general member smooth, giving a complete classification. Under the additional hypothesis that all members are irreducible, we prove that there exists a unique non-isotrivial pencil with these properties up to projective transformation. We compare our construction with the classical approaches given by Gattazzo, Beauville and Miranda-Persson. |
| title | Pencils of plane cubics with one base point |
| topic | Algebraic Geometry 14C21, 14H50, 14H10 |
| url | https://arxiv.org/abs/2407.04569 |