Hilbert scheme of smooth curves of degree sixteen in ℙ⁵

2025/03/24 by Keem, Changho
#14C05 #14H10 #Algebraic Geometry (math.AG) #FOS: Mathematics

paper · doi:10.48550/arxiv.2503.18428

Abstract

We denote by H_d,g,r the Hilbert scheme of smooth curves, which is the union of components whose general point corresponds to a smooth irreducible and non-degenerate curve of degree d and genus g in ℙ^r. In this article, we study H_16,g,5 for almost every possible genus g and chasing after its irreducibility. We also study the natural moduli map H_d,g,5\stackrelμ→M_g and several key properties such as gonality of a general element as well as characterizing smooth elements in each component.

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