Space curves which are the intersection of a cone with another surface
type: Item
instance of: scholarly article
title: Space curves which are the intersection of a cone with another surface
zbMATH Open document ID: 0677.14011
DOI: 10.1215/S0012-7094-88-05738-9
author: David B. Jaffe
published in: Duke Mathematical Journal
publication date: 1988-01-01T00:00:00Z
review text: Let \(S\subseteq {\mathbb{P}}^ 3\) be a cone and let \(C\subseteq S\) be a smooth curve. This paper gives necessary and sufficient conditions for there to exist a surface \(T\subseteq {\mathbb{P}}^ 3\) such that \(C=S\cap T\) as sets. In this case C is called a set-theoretic intersection on S. The conditions are phrased in terms of the interaction between C and a generic hyperplane section D of S. For example, if the base field has characteristic zero and the vertex of S is not on C, then C is a set- theoretic complete intersection on S if and only if D is smooth. One consequence of this characterization, is the proof that, in characteristic zero, a smooth monomial curve of degree at least four cannot be a set-theoretic complete intersection on a cone.
Mathematics Subject Classification ID: 14M10
Mathematics Subject Classification ID: 14H45
zbMATH DE Number: 4108913
zbMATH Keywords: cone
zbMATH Keywords: set-theoretic intersection
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 4108913