On birational monomial transformations of plane
type: Item
instance of: scholarly article
title: On birational monomial transformations of plane
zbMATH Open document ID: 1069.14016
DOI: 10.1155/S0161171204306514
author: A. B. Korchagin
published in: International Journal of Mathematics and Mathematical Sciences
publication date: 2005-05-18T00:00:00Z
full work available at URL: https://eudml.org/doc/51549
review text: Summary: We study birational monomial transformations of the form \(\varphi(x:y:z)=(\varepsilon_1x^{\alpha_1}y^{\beta_1}z^{\gamma_1}: \varepsilon_2x^{\alpha_2}y^{\beta_2}z^{\gamma_2} : x^{\alpha_3}y^{\beta_3}z^{\gamma_3})\), where \(\varepsilon_1, \varepsilon_2 \in \{-1, 1\}\). These transformations form a group. We describe this group in terms of generators and relations and, for every such transformation \(\varphi\), we prove a formula, which represents the transformation \(\varphi\) as a product of generators of the group. To prove this formula, we use birationally equivalent polynomials \(Ax + By + C\) and \(Ax^p + By^q + Cx^ry^s\). If \(\varphi\) is the transformation which carries one polynomial onto another, then the integral powers of generators in the product, which represents the transformation \(\varphi\), can be calculated by the expansion of \(p/q\) in the continued fraction.
Mathematics Subject Classification ID: 14E07
zbMATH DE Number: 2168717
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 2168717