Implicitization of de Jonquières parametrizations

One introduces a class of projective parameterizations that resemble generalized de Jonquières maps. Any such parametrization defines a birational map \(\mathfrak{F}\) of \(\pp^n\) onto a hypersurface \(V(F)\subset \pp^{n+1}\) with a strong handle to implicitization. From this side, the theory here developed extends recent work of Ben\ii tez--D'Andrea on monoid parameterizations. The paper deals with both ideal theoretic and effective aspects of the problem. The ring theoretic development gives information on the Castelnuovo--Mumford regularity of the base ideal of \(\mathfrak{F}\). From the effective side, one gives an explicit formula of \(\deg(F)\) involving data from the inverse map of \(\mathfrak{F}\) and show how the present parametrization relates to monoid parameterizations.