Hilbert function of powers of ideals of low codimension
type: Item
instance of: scholarly article
title: Hilbert function of powers of ideals of low codimension
zbMATH Open document ID: 0927.13020
DOI: 10.1007/PL00004716
published in: Mathematische Zeitschrift
publication date: 1999-09-14T00:00:00Z
review text: We study the relationship between the Hilbert function of an ideal \(I\) and that of its powers \(I^k\) where \(I\) is either Cohen-Macaulay of codimension 2 or Gorenstein of codimension 3. We show that if \(I\) is an ideal in one of these two classes and it is of linear type then the Hilbert function of \(I^k\) depends only on the Hilbert function of \(I\). In other words, if we assume that \(I\) and \(J\) are either Cohen-Macaulay of codimension 2 or Gorenstein of codimension 3 ideals, and that they are both of linear type and they have the same Hilbert function then also the powers \(I^k\) and \(J^k\) have the same Hilbert function for all \(k\).
Mathematics Subject Classification ID: 13D40
Mathematics Subject Classification ID: 13A15
Mathematics Subject Classification ID: 13C14
zbMATH DE Number: 1336858
zbMATH Keywords: powers of ideals
zbMATH Keywords: low codimension
zbMATH Keywords: Hilbert function
zbMATH Keywords: Cohen-Macaulay
zbMATH Keywords: Gorenstein
author: Aldo Conca
author: G. Valla
MaRDI profile type: Publication
full work available at URL: pl00004716
OpenAlex ID: W2034683953
description: scientific article; zbMATH DE number 1336858