Irreducibility of the Hilbert scheme of smooth curves in \(\mathbb {P}^4\) of degree \(g+2\) and genus \(g\)
type: Item
instance of: scholarly article
title: Irreducibility of the Hilbert scheme of smooth curves in \(\mathbb {P}^4\) of degree \(g+2\) and genus \(g\)
zbMATH Open document ID: 1386.14104
author: Chang Ho Keem
author: Yun-Hwan Kim
published in: Archiv der Mathematik
publication date: 2017-11-30T00:00:00Z
review text: Let \(\mathcal H_{d,g,r}\) be the union of the Hilbert scheme components whose general point corresponds to a smooth irreducible and non-degenerate curve of degree d and genus g in \(\mathbb P^r\). In this paper the authors study \(\mathcal H_{d,g,r}\) for the case \(r =4\) and \(d = g+2\). The main result shows that any non-empty \(\mathcal H_{g+2,g,4}\) is irreducible without any restriction on \(g\). The same result was previously established by \textit{H. Iliev} [Proc. Am. Math. Soc. 134, No. 10, 2823--2832 (2006; Zbl 1097.14022)] with several low genus cases left untreated.
reviewed by: Dawei Chen
Mathematics Subject Classification ID: 14H10
Mathematics Subject Classification ID: 14C05
zbMATH DE Number: 6813951
zbMATH Keywords: Hilbert scheme
zbMATH Keywords: algebraic curves
zbMATH Keywords: linear series
MaRDI profile type: Publication
full work available at URL: s00013-017-1083-7
OpenAlex ID: W4233346605
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DOI: 10.1007/S00013-017-1083-7
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description: scientific article; zbMATH DE number 6813951