Geometry of linear determinantal quartic 3-folds via their intermediate Jacobian
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
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2025
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| _version_ | 1866916912723656704 |
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| author | Leal, Manuel Huerta, César Lozano Vite, Montserrat |
| author_facet | Leal, Manuel Huerta, César Lozano Vite, Montserrat |
| contents | A general linear determinantal quartic in $\mathbb{P}^4$ is nodal, non-$\mathbb{Q}$-factorial and rational. We show that the family $\mathcal{F}$ of such quartics also contains rational $\mathbb{Q}$-factorial quartics, and that a generic member of $\mathcal{F}$ can specialize to a rational non-$\mathbb{Q}$-factorial double quadric. We describe the birational geometry of these three types of 3-folds, showing that it is governed by the extrinsic geometry of a curve $C\subset \mathbb{P}^3$. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2504_14461 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Geometry of linear determinantal quartic 3-folds via their intermediate Jacobian Leal, Manuel Huerta, César Lozano Vite, Montserrat Algebraic Geometry 14E05 (Primary) 14E07, 14E08, 14E30, 14H45, 14H50, 14J30, 14M06, 14M12, 14M20 (Secondary) A general linear determinantal quartic in $\mathbb{P}^4$ is nodal, non-$\mathbb{Q}$-factorial and rational. We show that the family $\mathcal{F}$ of such quartics also contains rational $\mathbb{Q}$-factorial quartics, and that a generic member of $\mathcal{F}$ can specialize to a rational non-$\mathbb{Q}$-factorial double quadric. We describe the birational geometry of these three types of 3-folds, showing that it is governed by the extrinsic geometry of a curve $C\subset \mathbb{P}^3$. |
| title | Geometry of linear determinantal quartic 3-folds via their intermediate Jacobian |
| topic | Algebraic Geometry 14E05 (Primary) 14E07, 14E08, 14E30, 14H45, 14H50, 14J30, 14M06, 14M12, 14M20 (Secondary) |
| url | https://arxiv.org/abs/2504.14461 |