Irreducibility of the Hilbert scheme of smooth curves in \Bbb P⁴ of degree g+2 and genus g

2017/03/22 by Keem, Changho, Kim, Yun-Hwan
#14C05 #14H10 #Algebraic Geometry (math.AG) #FOS: Mathematics

paper · doi:10.48550/arxiv.1703.07516

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 \PP^r. In this note, we show that any non-empty H_g+2,g,4 is irreducible without any restriction on the genus g. Our result augments the irreducibility result obtained earlier by Hristo Iliev(2006), in which several low genus g≤ 10 cases have been left untreated.

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