Components of the Hilbert scheme of smooth space curves with the expected number of moduli
type: Item
instance of: scholarly article
title: Components of the Hilbert scheme of smooth space curves with the expected number of moduli
zbMATH Open document ID: 0682.14018
DOI: 10.1007/BF01173697
author: Giuseppe Pareschi
published in: Manuscripta Mathematica
publication date: 1989-01-01T00:00:00Z
full work available at URL: https://eudml.org/doc/155363
review text: Suppose that \(H^3_{d,g}\) is the Hilbert scheme of smooth curves of degree d and genus g in \({\mathbb{P}}^ 3\). If \(g\leq (d^{3/2}/(6\cdot 2^{1/2})+\text{ lower terms}),\) the author constructs a component V of \(H^ 3_{d,g}\) satisfying the following properties: 1. If C is a general curve of V, then \(H^ 1(N_{C/{\mathbb{P}}^ 3})=0\). Hence V is generically smooth and \(\dim (V)=4d.\) 2. The dimension of the image of V in the \(M_ g\), the moduli space of curve, is equal to \(\text{Min}(3g-3,3g-3-(\rho(d,g,3))\). The method of proof is by smoothing reducible nodal curves.
Mathematics Subject Classification ID: 14H10
Mathematics Subject Classification ID: 14C05
zbMATH DE Number: 4116695
zbMATH Keywords: Hilbert scheme
zbMATH Keywords: moduli space of curve
zbMATH Keywords: smoothing reducible nodal curves
reviewed by: Lawrence Ein
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 4116695