Construction of space curves with good properties
type: Item
instance of: scholarly article
title: Construction of space curves with good properties
zbMATH Open document ID: 0693.14018
DOI: 10.1007/BF01446556
author: Gunnar Fløystad
published in: Mathematische Annalen
publication date: 1991-01-01T00:00:00Z
full work available at URL: https://eudml.org/doc/164765
review text: We show that for all (d,g) in the degree, genus plane which are between a certain piecewise linear curve \(C_ K\) of order \(g\sim \frac{2\sqrt{2}}{3}d^{3/2}\) and a curve \(C_ 1\) of order \(g\sim \frac{2}{3}d^{3/2}\), there are smooth connected curves with degree d and genus g which are of maximal rank. We also show that for all (d,g) between the curve \(C_ K\) and the d- axis, there are smooth connected curves Y with degree d and genus g such that \(h^ 1I_ Y(n)\cdot h^ 2I_ Y(n)=0\) for all \(n\in {\mathbb{Z}}\). Together with a previous result of Sernesi this implies that for all (d,g) in this area there are components \(H_{d,g}\) of the Hilbert scheme with the expected number of moduli.
Mathematics Subject Classification ID: 14H50
Mathematics Subject Classification ID: 14N05
Mathematics Subject Classification ID: 14C05
zbMATH DE Number: 4134215
zbMATH Keywords: curves with maximal rank
zbMATH Keywords: Hilbert scheme
zbMATH Keywords: number of moduli
MaRDI profile type: Publication
cites work: The maximal rank conjecture for non special curves in \({\mathbb{P}}^ 3\)
cites work: Classification of maximal rank curves in the liaison class \(L_ n\)
cites work: Q3689280
cites work: Sur la postulation generique des courbes rationnelles
cites work: Components of the Hilbert scheme of smooth space curves with the expected number of moduli
cites work: On the existence of certain families of curves
cites work: Curves on surfaces with multiple line.
Recommended article: Q3222976
Recommended article: Construction of minimal families of space curves
Recommended article: Constructive curves in non-Euclidean planes
Recommended article: On space curves with good cohomological properties
Recommended article: Q4342939
Recommended article: Q3709463
Recommended article: Space curves with a prescribed index of regularity
description: scientific article; zbMATH DE number 4134215