A simple counterexample to Kouchnirenko's conjecture
type: Item
instance of: scholarly article
title: A simple counterexample to Kouchnirenko's conjecture
zbMATH Open document ID: 1012.12001
author: Bertrand Haas
published in: Beiträge zur Algebra und Geometrie
publication date: 2002-08-20T00:00:00Z
full work available at URL: https://eudml.org/doc/232052
full work available at URL: 1.html
review text: The author gives a counter-example to a conjecture of Kouchnirenko on an upper bound for the number of nondegenerate isolated positive roots of a system of \(k\) polynomial equations in \(k\) variables \(f_1 = \cdots = f_q = 0\). The conjecture states that if \(m_i\) is the number of terms in \(f_i\), then \((m_1-1)\cdots(m_k-1)\) is an upper bound. In the counter-example cases are considered with \(k=2\) and \(m_1 = m_2 = 3\) and it is proved that there exist \(5\) positive solutions. The author discusses possible alternative upper bounds.
reviewed by: Doru Ştefănescu
Mathematics Subject Classification ID: 12D10
Mathematics Subject Classification ID: 65H10
Mathematics Subject Classification ID: 14M10
zbMATH DE Number: 1784588
zbMATH Keywords: systems of polynomial equations
zbMATH Keywords: Descartes' rule
describes a project that uses: PHCpack
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 1784588