Implicitization of de Jonquières parametrizations (Q405379)

A de Jonquières parametrization \({\mathcal F}\) of a hypersurface is derived from a given Cremona map of \(n\)-dimensional projective space onto itself. Such parametrizations are specials forms of rational parametrizations. They can also be seen as generalizations of monoid parametrizations.NEWLINENEWLINE The goal of this paper is to derive the implicit equation \(F=0\) for the hypersurface from the data involved in a de Jonquières parametrization \({\mathcal F}\); or, in any case, as much information about the defining polynomial \(F\) as possible. So, for instance, a formula for the degree of \(F\) is given. Furthermore, the relation between the present parametrization and monoid parametrizations is exhibited.NEWLINENEWLINE An indication of which aspects of the treatment can be carried out algorithmically, and how, would definitely increase the value of this approach.