On birational monomial transformations of plane

Anatoly B. Korchagin

International Journal of Mathematics and Mathematical Sciences, 2004, vol. 2004, 1-7

Abstract:

We study birational monomial transformations of the form φ ( x : y : z ) = ( ϵ 1 x α 1 y β 1 z γ 1 : ϵ 2 x α 2 y β 2 z γ 2 : x α 3 y β 3 z γ 3 ) , where ϵ 1 , ϵ 2 ∈ { − 1 , 1 } . These transformations form a group. We describe this group in terms of generators and relations and, for every such transformation φ , we prove a formula, which represents the transformation φ as a product of generators of the group. To prove this formula, we use birationally equivalent polynomials A x + B y + C and A x p + B y q + C x r y s . If φ is the transformation which carries one polynomial onto another, then the integral powers of generators in the product, which represents the transformation φ , can be calculated by the expansion of p / q in the continued fraction.

Date: 2004
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jijmms:438417

DOI: 10.1155/S0161171204306514

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