On set theoretic complete intersections in \({\mathbb{P}}^ 3\)
type: Item
instance of: scholarly article
title: On set theoretic complete intersections in \({\mathbb{P}}^ 3\)
zbMATH Open document ID: 0661.14027
DOI: 10.1007/BF01442680
author: David B. Jaffe
published in: Mathematische Annalen
publication date: 1989-01-01T00:00:00Z
full work available at URL: https://eudml.org/doc/164593
review text: Let \(S\subset {\mathbb{C}}{\mathbb{P}}^ 3\) be a surface satisfying one of the following conditions: either it has at most ordinary nodes as singularities, or it has degree at most three, or it is a cone. Let \(D\subset S\) be a smooth curve. Assume that there exists another surface T such that \(D=S\cap T\) as sets. Under these conditions, we prove that degree\((D)\leq genus\)(D)\(+3\).
Mathematics Subject Classification ID: 14H45
Mathematics Subject Classification ID: 14N05
Mathematics Subject Classification ID: 14M10
zbMATH DE Number: 4079608
zbMATH Keywords: set theoretic complete intersection
zbMATH Keywords: degree
zbMATH Keywords: genus
zbMATH Keywords: space curve
MaRDI profile type: Publication
cites work: On Isolated Rational Singularities of Surfaces
cites work: Q5749404
cites work: No rational nonsingular quartic curve \({\mathcal C}_ 4\subset {\mathbb{P}}^ 3\) can be set-theoretic complete intersection on a cubic surface
cites work: Fifteen characterizations of rational double points and simple critical points
cites work: Q4143433
cites work: Complete Intersections in Characteristic p > 0
cites work: Space curves which are the intersection of a cone with another surface
cites work: The topology of normal singularities of an algebraic surface and a criterion for simplicity
cites work: Elementary transformations of Dynkin graphs and singularities on quartic surfaces
OpenAlex ID: W4251318678
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description: scientific article; zbMATH DE number 4079608