Liaison and deformation
type: Item
instance of: scholarly article
title: Liaison and deformation
zbMATH Open document ID: 0575.13013
DOI: 10.1016/0022-4049(86)90143-X
author: Bernd Ulrich
published in: Journal of Pure and Applied Algebra
publication date: 1986-01-01T00:00:00Z
review text: The relation between liaison and some notions from deformation theory (as rigidity, the number of generators of the normal module, smoothability) is studied. Let \(P=kX\) be a power series ring over a field k of characteristic zero. Let I be a perfect P-ideal and let J be geometrically linked to I with respect to a regular sequence \(\alpha\). Upper and lower bounds are established for the number of generators of the normal module \(Hom_ P(J,P/J)\) in terms of the number of generators of \(Hom_ P(I,P/I)\). The number of generators of some normal modules are computed. Let I and J be perfect P-ideals in the same linkage class. It is algebraically proved that P/I is smoothable in codimension \(s\geq 3\) iff P/J has the same property.
Mathematics Subject Classification ID: 13D10
Mathematics Subject Classification ID: 13A15
zbMATH DE Number: 3918522
zbMATH Keywords: linkage
zbMATH Keywords: liaison
zbMATH Keywords: deformation theory
zbMATH Keywords: rigidity
zbMATH Keywords: number of generators
zbMATH Keywords: smoothability
reviewed by: Ketty Peeva
MaRDI profile type: Publication
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full work available at URL: 0022-4049(86)90143-x
OpenAlex ID: W2048607931
description: scientific article; zbMATH DE number 3918522