The Noether-Lefschetz locus of surfaces in \(\mathbb{P}^3\) formed by determinantal surfaces

We study the components of the family of determinantal degree \(d\) surfaces in \(\mathbb{P}^3\). We compute their dimensions and show that each of them contains a component of the Noether-Lefschetz locus \(NL(d)\). Our computations exhibit that determinantal surfaces in \(\mathbb{P}^3\) of degree 4...

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Bibliographic Details
Published inarXiv.org
Main Authors Leal, Manuel, César Lozano Huerta, Vite, Montserrat
Format Paper
LanguageEnglish
Published Ithaca Cornell University Library, arXiv.org 07.11.2023
Subjects
Hyperspaces
Polynomials
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Summary:We study the components of the family of determinantal degree \(d\) surfaces in \(\mathbb{P}^3\). We compute their dimensions and show that each of them contains a component of the Noether-Lefschetz locus \(NL(d)\). Our computations exhibit that determinantal surfaces in \(\mathbb{P}^3\) of degree 4 form a divisor in \(|\mathcal{O}_{\mathbb{P}^3}(4)|\) with 5 irreducible components. The degrees of these components, we will compute, are \(320,2508,136512,38475,320112\).
ISSN:2331-8422