On the Hilbert scheme of smooth curves of degree d=15 in ℙ⁵

2023/10/01 by Ballico, Edoardo, Keem, Changho
#Algebraic Geometry (math.AG) #FOS: Mathematics #Primary 14C05 #Secondary 14H10

paper · doi:10.48550/arxiv.2310.00682

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_15,g,5 for every possible genus g and determine when it is irreducible. We also study the moduli map H_15,g,5\rightarrowM_g and several key properties such as gonality of a general element as well as characterizing smooth elements of each component.

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