Degrevlex Gröbner bases of generic complete intersections.
type: Item
instance of: scholarly article
title: Degrevlex Gröbner bases of generic complete intersections.
zbMATH Open document ID: 1062.13007
DOI: 10.1016/S0022-4049(02)00297-9
author: Guillermo Moreno-Socías
published in: Journal of Pure and Applied Algebra
publication date: 2003-05-27T00:00:00Z
review text: A generic standard graded algebra is an algebra \(K[X_1,\dots,X_n]/(g_1,\dots, g_m)\) where \(g_1,\dots,g_m\) are generic polynomials over a field \(K\). Let \(A\) be a generic algebra which is a complete intersection. Starting from the Hilbert Samuel function of \(A\), which is well known, the author studies the Hilbert-Samuel function of \(A\) refined by an \((\ell)\)-adic filtration, \(\ell\) being a linear form. As an application he obtains a structure theorem which describes the stairs of such algebras with respect to the degree reverse-lexicographic order. Moreover a conjecture is stated on the Gröbner bases of \(A\) with respect to the degree reverse-lexicographic order, and it is proved in some special cases.
reviewed by: Emanuela De Negri
Mathematics Subject Classification ID: 13P10
Mathematics Subject Classification ID: 13D40
zbMATH DE Number: 1917888
zbMATH Keywords: generic algebra
zbMATH Keywords: complete intersection
zbMATH Keywords: Hilbert-Samuel function
zbMATH Keywords: degree reverse-lexicographic order
zbMATH Keywords: degrevlex Gröbner basis
MaRDI profile type: Publication
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full work available at URL: s0022-4049(02)00297-9
OpenAlex ID: W2091651798
description: scientific article; zbMATH DE number 1917888