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

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  • Manuel Leal
  • César Lozano Huerta
  • Montserrat Vite

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$\hskip.001pt 320112$.

Suggested Citation

  • Manuel Leal & César Lozano Huerta & Montserrat Vite, 2024. "The Noether–Lefschetz locus of surfaces in P3${\mathbb {P}}^3$ formed by determinantal surfaces," Mathematische Nachrichten, Wiley Blackwell, vol. 297(12), pages 4671-4688, December.
    • Handle: RePEc:bla:mathna:v:297:y:2024:i:12:p:4671-4688
    DOI: 10.1002/mana.202400132
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