On birational monomial transformations of plane
We study birational monomial transformations of the form φ(x:y:z)=(ϵ1xα1yβ1zγ1:ϵ2xα2yβ2zγ2:xα3yβ3zγ3), where ϵ1,ϵ2∈{−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 tr...
| Main Author: | |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Hindawi Limited
2004-01-01
|
| Series: | International Journal of Mathematics and Mathematical Sciences |
| Online Access: | http://dx.doi.org/10.1155/S0161171204306514 |
| Summary: | We study birational monomial transformations of the form φ(x:y:z)=(ϵ1xα1yβ1zγ1:ϵ2xα2yβ2zγ2:xα3yβ3zγ3), where ϵ1,ϵ2∈{−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 Ax+By+C and Axp+Byq+Cxrys. 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. |
|---|---|
| ISSN: | 0161-1712 1687-0425 |