The Noether–Lefschetz locus of surfaces in P3${\mathbb {P}}^3$ formed by determinantal surfaces

Manuel Leal, César Lozano Huerta and Montserrat Vite

Mathematische Nachrichten, 2024, vol. 297, issue 12, 4671-4688

Abstract: We compute the dimension of certain components of the family of smooth determinantal degree d$d$ surfaces in P3${\mathbb {P}}^3$, and show that each of them is the closure of a component of the Noether–Lefschetz locus NL(d)$NL(d)$. Our computations exhibit that smooth determinantal surfaces in P3${\mathbb {P}}^3$ of degree 4 form a divisor in |OP3(4)|$|\mathcal {O}_{{\mathbb {P}}^3}(4)|$ with five irreducible components. We will compute the degrees of each of these components: 320,2508,136512,38475$320,2508,136512,38475$, and 320112$\hskip.001pt 320112$.

Date: 2024
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