Sets of points and their conductor
type: Item
instance of: scholarly article
title: Sets of points and their conductor
zbMATH Open document ID: 1119.13011
author: Laura Bazzotti
published in: Journal of Algebra
publication date: 2005-02-22T00:00:00Z
review text: Let \(X\) be a set of distinct \(k\)-rational points in the \(n\)-dimensional projective space. If \(P\in X\) the minimal degree of an hypersurface which vanishes at every points of \(X\setminus\{P\},\) but not at \(P\) is called the separating degree of \(P.\) The socle values of \(X,\) \(\xi_1>\xi_2>\ldots>\xi_t,\) are the possible values of the separating degrees of the points of \(X.\) For every \(j\) let \(X_j\) be the subset of \(X\) whose points have separating degree equal to \(\xi_j.\) In this paper the author determines the ideal \(I(X_1\cup\ldots\cup X_j)\) for every \(j.\) Moreover, when \(X\subset{\mathbb P}^2,\) the author finds a sharp lower bound for the dimension of the algebra defined by the conductor of the coordinate ring of \(X.\)
Mathematics Subject Classification ID: 13D02
Mathematics Subject Classification ID: 13D40
zbMATH DE Number: 2136610
zbMATH Keywords: set of points
zbMATH Keywords: conductor
zbMATH Keywords: degree matrix
reviewed by: Giuseppe Zappalà
MaRDI profile type: Publication
full work available at URL: j.jalgebra.2004.09.031
OpenAlex ID: W2044430088
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DOI: 10.1016/J.JALGEBRA.2004.09.031
description: scientific article; zbMATH DE number 2136610