The second fundamental form of the moduli space of cubic threefolds in $\mathcal A_5$
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arXiv
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| Autores principales: | , , , |
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| Formato: | Preprint |
| Publicado: |
2022
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| Acceso en línea: | |
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| _version_ | 1866914603049418752 |
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| author | Colombo, Elisabetta Frediani, Paola Naranjo, Juan Carlos Pirola, Gian Pietro |
| author_facet | Colombo, Elisabetta Frediani, Paola Naranjo, Juan Carlos Pirola, Gian Pietro |
| contents | We study the second fundamental form of the Siegel metric in $\mathcal A_5$ restricted to the locus of intermediate Jacobians of cubic threefolds. We prove that the image of this second fundamental form, which is known to be non-trivial, is contained in the kernel of a suitable multiplication map. Some ingredients are: the conic bundle structure of cubic threefolds, Prym theory, Gaussian maps and Jacobian ideals. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2207_13432 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | The second fundamental form of the moduli space of cubic threefolds in $\mathcal A_5$ Colombo, Elisabetta Frediani, Paola Naranjo, Juan Carlos Pirola, Gian Pietro Algebraic Geometry 14J30, 14J10, 32G20, 14H40 We study the second fundamental form of the Siegel metric in $\mathcal A_5$ restricted to the locus of intermediate Jacobians of cubic threefolds. We prove that the image of this second fundamental form, which is known to be non-trivial, is contained in the kernel of a suitable multiplication map. Some ingredients are: the conic bundle structure of cubic threefolds, Prym theory, Gaussian maps and Jacobian ideals. |
| title | The second fundamental form of the moduli space of cubic threefolds in $\mathcal A_5$ |
| topic | Algebraic Geometry 14J30, 14J10, 32G20, 14H40 |
| url | https://arxiv.org/abs/2207.13432 |