Hilbert function and resolution of the powers of the ideal of the rational normal curve
type: Item
instance of: scholarly article
title: Hilbert function and resolution of the powers of the ideal of the rational normal curve
zbMATH Open document ID: 0985.13007
DOI: 10.1016/S0022-4049(99)00146-2
author: Aldo Conca
published in: Journal of Pure and Applied Algebra
publication date: 2002-05-14T00:00:00Z
review text: The author studies the ideals mentioned in the title. If \(P\) denotes the ideal defining the rational normal curve, he computes the regularity of the power \(P^h\) and the symbolic power \(P^{(h)}\). Then he proceeds to find the Hilbert function, the Hilbert polynomial, and the Betti numbers of \(P^h\). In the case of \(P^{(h)}\), his calculation works only for \(h\leq 3\) or for \(n\leq 4\). Finally the Hilbert function of the module of Kähler differentials of \(K[x_0,\dots, x_n]/P\) is derived from \(P^{(2)}\).
reviewed by: Martin Kreuzer
Mathematics Subject Classification ID: 13D40
Mathematics Subject Classification ID: 13D02
Mathematics Subject Classification ID: 13C40
Mathematics Subject Classification ID: 14M12
Mathematics Subject Classification ID: 14H99
zbMATH DE Number: 1517291
zbMATH Keywords: powers of ideal
zbMATH Keywords: ideal of rational normal curve
zbMATH Keywords: linear resolution
zbMATH Keywords: Hilbert function
zbMATH Keywords: Hilbert polynomial
describes a project that uses: CoCoA
MaRDI profile type: Publication
cites work: Resolutions of determinantal ideals: The submaximal minors
cites work: Q4274969
cites work: Straightening law and powers of determinantal ideals of Hankel matrices
cites work: Sagbi bases with applications to blow-up algebras.
cites work: Linear free resolutions and minimal multiplicity
cites work: Graded Betti numbers of some embedded rational \(n\)-folds
Recommended article: Hilbert function of powers of ideals of low codimension
Recommended article: Regularity index of Hilbert functions of powers of ideals
Recommended article: Normalization of monomial ideals and Hilbert functions
Recommended article: On the Hilbert function of certain rings of monomial curves
Recommended article: Hilbert functions of \(d\)-regular ideals
Recommended article: Hilbert-Kunz function of monomial ideals and binomial hypersurfaces
Recommended article: Hilbert functions, residual intersections, and residually \(S_2\) ideals
Recommended article: On Hilbert functions of general intersections of ideals
Recommended article: Hilbert polynomials and powers of ideals
Recommended article: Hilbert-Kunz functions for normal rings
description: scientific article; zbMATH DE number 1517291