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

IF 0.8 3区数学 Q2 MATHEMATICS

Mathematische Nachrichten Pub Date : 2024-10-09 DOI:10.1002/mana.202400132

Manuel Leal, César Lozano Huerta, Montserrat Vite

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引用次数: 0

Abstract

We compute the dimension of certain components of the family of smooth determinantal degree $d$ surfaces in $P^{3}$ , and show that each of them is the closure of a component of the Noether–Lefschetz locus $N L (d)$ . Our computations exhibit that smooth determinantal surfaces in $P^{3}$ of degree 4 form a divisor in $| O_{P^{3}} (4) |$ with five irreducible components. We will compute the degrees of each of these components: $320, 2508, 136512, 38475$ , and $320112$ .

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来源期刊

Mathematische Nachrichten 数学-数学

CiteScore

1.50

自引率

0.00%

发文量

157

审稿时长

4-8 weeks

期刊介绍： Mathematische Nachrichten - Mathematical News publishes original papers on new results and methods that hold prospect for substantial progress in mathematics and its applications. All branches of analysis, algebra, number theory, geometry and topology, flow mechanics and theoretical aspects of stochastics are given special emphasis. Mathematische Nachrichten is indexed/abstracted in Current Contents/Physical, Chemical and Earth Sciences; Mathematical Review; Zentralblatt für Mathematik; Math Database on STN International, INSPEC; Science Citation Index