Conic linear series and pencils of plane quartics
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arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866911263728074752 |
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| author | Moschetti, Riccardo Pirola, Gian Pietro Stoppino, Lidia |
| author_facet | Moschetti, Riccardo Pirola, Gian Pietro Stoppino, Lidia |
| contents | We study linear systems cut out by cones of fixed degree on a smooth complex curve $C\subset\mathbb{P}^{3}$. We develop a systematic study of the families of such systems, considering their limits, their infinitesimal behaviour and some associated geometric structures. As an application, we prove the existence of a non-isotrivial pencil of quartics with only one base point, all whose members are irreducible and whose general member is smooth. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2511_10327 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Conic linear series and pencils of plane quartics Moschetti, Riccardo Pirola, Gian Pietro Stoppino, Lidia Algebraic Geometry 14H50, 14C21, 14H10, 14C20 We study linear systems cut out by cones of fixed degree on a smooth complex curve $C\subset\mathbb{P}^{3}$. We develop a systematic study of the families of such systems, considering their limits, their infinitesimal behaviour and some associated geometric structures. As an application, we prove the existence of a non-isotrivial pencil of quartics with only one base point, all whose members are irreducible and whose general member is smooth. |
| title | Conic linear series and pencils of plane quartics |
| topic | Algebraic Geometry 14H50, 14C21, 14H10, 14C20 |
| url | https://arxiv.org/abs/2511.10327 |