Nonsingular curves passing through points of \({\mathbb{P}}^ 2\) in generic position. I
type: Item
instance of: scholarly article
title: Nonsingular curves passing through points of \({\mathbb{P}}^ 2\) in generic position. I
zbMATH Open document ID: 0556.14010
DOI: 10.1016/0021-8693(85)90153-X
author: Renato Maggioni
author: Alfio Ragusa
published in: Journal of Algebra
publication date: 1985-01-01T00:00:00Z
review text: The paper investigates the following question: given n points in \({\mathbb{P}}^ 2\), subject to some condition of ''genericity'', what is the least integer \(\delta\) such that there is a nonsingular curve of degree less or equal to \(\delta\) passing through the points? An evaluation for \(\delta\) is given when no three of the points are on a line. The value of \(\delta\) is also obtained if different notions of general position for n points are considered [see for instance \textit{A. V. Geramita} and \textit{F. Orecchia}, J. Algebra 70, 116-140 (1981; Zbl 0464.14007)]. Special attention is paid to points in uniform position: it is shown that if \(n=\left( \begin{matrix} d+2\\ 2\end{matrix} \right)+h\), \(0\leq h\leq 2\) and n points are in uniform position, then \(\delta =d+1\). Analogous results are proved for other ranges of h. Many examples are also discussed. [For part II see the following review.]
Mathematics Subject Classification ID: 14H99
Mathematics Subject Classification ID: 14N10
zbMATH DE Number: 3886037
zbMATH Keywords: general position of points
reviewed by: Paolo Valabrega
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 3886037