Minimal generation of ideals of algebraic varieties at points with multilinear tangent cones
type: Item
instance of: scholarly article
title: Minimal generation of ideals of algebraic varieties at points with multilinear tangent cones
zbMATH Open document ID: 1327.13022
author: F. Orecchia
author: Isabella Ramella
published in: Ricerche di Matematica
publication date: 2014-12-08T00:00:00Z
review text: Let \(V\subset \mathbb A^n\) be an affine variety defined over an algebraically closed field of characteristic \(0\). let \(P\in V\) be an isolated singularity of \(V\). The authors assume that the normalization of \(V\) is regular at \(P\) and that the tangent cone \(W\) of \(V\) at \(P\) consists of a union of linear spaces, all of the same dimension. With the assumptions, the authors prove that the minimal number of generators for the local ideal at \(P\) of \(V\) equals the minimal number of generators for the ideal of \(W\). The result extends to varieties \(V\) of arbitrary dimension a previous theorem of the authors, limited to the case \(\dim(V)=1,2\).
reviewed by: Luca Chiantini
Mathematics Subject Classification ID: 13A30
Mathematics Subject Classification ID: 14J17
zbMATH DE Number: 6378249
zbMATH Keywords: tangent cone
MaRDI profile type: Publication
full work available at URL: s11587-014-0205-9
OpenAlex ID: W1988497804
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DOI: 10.1007/S11587-014-0205-9
description: scientific article; zbMATH DE number 6378249