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

Abstract

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 $320112$.

15 pages, 2 tables

References in corpus (1)

• On the dimension of the locus of determinantal hypersurfaces