A generic effective Nullstellensatz
type: Item
instance of: scholarly article
title: A generic effective Nullstellensatz
zbMATH Open document ID: 1082.13013
author: Ravikiran Rajagopal
author: Lee C. Potter
published in: Linear Algebra and its Applications
publication date: 2005-05-04T00:00:00Z
review text: J. Kollár has proved the following theorem, known as effective Nullstellensatz: Theorem. Let \(F\) be a field, and \(h_{1 },\dots,h_{M}\in F[x_{1},\dots,x_{n} ] \) with maximum total degree \(\delta\) such that \((h_{1 },\dots,h_{M})= F[x_{1},\dots,x_{n} ] \). Then there exists \(g_{1 },\dots,g_{M}\in F[x_{1},\dots,x_{n} ] \) with maximum total degree \(\delta^{ \min (n,M) } \) such that \(\sum_{i=1}^M g_{i} h_{i} =1\). The aim of this paper is to give a generic effective Nullstellensatz, that is assuming that \(h_{1 },\dots,h_{M}\) are generic. In this case the generic bound is small and is linear in the degrees of the polynomials. Also the set \(\{g_{1 },\dots,g_{M}\}\) is obtained by linear algebra.
reviewed by: Marcel Morales
Mathematics Subject Classification ID: 13F20
Mathematics Subject Classification ID: 14A05
zbMATH DE Number: 2165346
zbMATH Keywords: generic effective Nullstellensatz
zbMATH Keywords: polynomial degrees
MaRDI profile type: Publication
full work available at URL: j.laa.2004.11.007
OpenAlex ID: W2093609535
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DOI: 10.1016/J.LAA.2004.11.007
description: scientific article; zbMATH DE number 2165346