Some results on the surjectivity of surface parametrizations

This paper deals with the decision problem of the surjectivity of a rational surface parametrization. We give sufficient conditions for a parametrization to be surjective, and we describe different families of parametrizations that satisfy these criteria. In addition, we consider the problem of computing a superset of the points not covered by the parametrization. In this context, we report on the case of parametrizations without projective base points and we analyze the particular case of rational ruled surfaces.Ministerio de Economía y Competitivida