Covering of surfaces parametrized without projective base points

Abstract

We prove that every a ne rational surface, parametrized by means of an a ne rational parametrization without projective base points, can be covered by at most three parametrizations. Moreover, we give explicit formulas for computing the coverings. We provide two di erent approaches: either covering the surface with a surface parametrization plus a curve parametrization plus a point, or with the original parametrization plus two surface reparametrizations of it.