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| Auteurs principaux: | , , |
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| Format: | Preprint |
| Publié: |
2023
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| Accès en ligne: | https://arxiv.org/abs/2303.09028 |
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| _version_ | 1866929572402954240 |
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| author | Leal, Manuel Huerta, César Lozano Vite, Montserrat |
| author_facet | Leal, Manuel Huerta, César Lozano Vite, Montserrat |
| contents | We compute the dimension of certain components of the family of smooth determinantal degree $d$ surfaces in $\mathbb{P}^3$, and show that each of them is the closure of a component of the Noether-Lefschetz locus $NL(d)$. Our computations exhibit that smooth determinantal surfaces in $\mathbb{P}^3$ of degree 4 form a divisor in $|\mathcal{O}_{\mathbb{P}^3}(4)|$ with 5 irreducible components. We will compute the degrees of each of these components: $320,2508,136512,38475$ and $320112$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2303_09028 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | The Noether-Lefschetz locus of surfaces in $\mathbb{P}^3$ formed by determinantal surfaces Leal, Manuel Huerta, César Lozano Vite, Montserrat Algebraic Geometry We compute the dimension of certain components of the family of smooth determinantal degree $d$ surfaces in $\mathbb{P}^3$, and show that each of them is the closure of a component of the Noether-Lefschetz locus $NL(d)$. Our computations exhibit that smooth determinantal surfaces in $\mathbb{P}^3$ of degree 4 form a divisor in $|\mathcal{O}_{\mathbb{P}^3}(4)|$ with 5 irreducible components. We will compute the degrees of each of these components: $320,2508,136512,38475$ and $320112$. |
| title | The Noether-Lefschetz locus of surfaces in $\mathbb{P}^3$ formed by determinantal surfaces |
| topic | Algebraic Geometry |
| url | https://arxiv.org/abs/2303.09028 |