No rational nonsingular quartic curve \({\mathcal C}_ 4\subset {\mathbb{P}}^ 3\) can be set-theoretic complete intersection on a cubic surface
type: Item
instance of: scholarly article
title: No rational nonsingular quartic curve \({\mathcal C}_ 4\subset {\mathbb{P}}^ 3\) can be set-theoretic complete intersection on a cubic surface
zbMATH Open document ID: 0706.14031
author: Pier Carlo Craighero
author: Remo Gattazzo
published in: Rendiconti del Seminario Matematico della Università di Padova
publication date: 1989-01-01T00:00:00Z
full work available at URL: http://www.numdam.org/item
full work available at URL: https://eudml.org/doc/108133
review text: Generalizing a result of \textit{E. Stagnaro} [Rend. Accad. Naz. Sci. Detta XL, V. Ser. Mem. Mat. 7, No.1, 51-87 (1983; Zbl 0545.14025)], the authors show that smooth rational quartic curves in \({\mathbb{P}}_ k^ 3\) (k algebraically closed of \(char(k)=0)\) are never set-theoretic complete intersections of any pairs of surfaces \(F_ 3\) and \(F_ n\), for every degree n.
Mathematics Subject Classification ID: 14M10
Mathematics Subject Classification ID: 14H50
Mathematics Subject Classification ID: 14M20
zbMATH DE Number: 4158826
zbMATH Keywords: quartic curves
zbMATH Keywords: set-theoretic complete intersections
reviewed by: Manfred Herrmann
MaRDI profile type: Publication
cites work: Q4143433
cites work: Una osservazione sulla curva di Cremona di \(P^ 3_ k\) \(C:\{\lambda \mu^ 3,\lambda^ 3\mu,\lambda^ 4,\mu^ 4\}\)
cites work: The curve \({\tilde{\mathcal C}}_ 4=(\lambda^ 4,\lambda^ 3\mu,\lambda\mu^ 3,\mu^ 4)\subset {\mathbb{P}}^ 3_ k\), is not set- theoretic complete intersection of two quartic surfaces
cites work: Space curves which are the intersection of a cone with another surface
cites work: Q3869440
cites work: Some properties of complete intersections in “good” projective varieties
cites work: Q4137299
cites work: Q3335894
Recommended article: The curve \({\tilde{\mathcal C}}_ 4=(\lambda^ 4,\lambda^ 3\mu,\lambda\mu^ 3,\mu^ 4)\subset {\mathbb{P}}^ 3_ k\), is not set- theoretic complete intersection of two quartic surfaces
Recommended article: Surfaces in \(\mathbb{P}^4\) with no quadrisecant lines
Recommended article: Q4253905
Recommended article: Some Quartic Curves with no Points in any Cubic Field
Recommended article: Q3335894
Recommended article: Non-existence of smooth rational curves of degree d = 13, 14, 15 con-tained in a general quintic hypersurface of P4 and in some quadric hypersurface
Recommended article: Rational Normal Curves as Set-Theoretic Complete Intersections of Quadrics
Recommended article: Rational surfaces in \({\mathbb{P}}^4\) containing a plane curve
Recommended article: Fourth degree monoidal surfaces of \({\mathbb{P}}^ 3_ k\) having complete intersection subset curves
Recommended article: Non-rationality of the 4-dimensional smooth complete intersection of a quadric and a quartic not containing planes
description: scientific article; zbMATH DE number 4158826