Covering of surfaces parametrized without projective base points

This is the author's version of the work. It is posted here for your personal use. Not for redistribution. The definitive Version of Record was published in "Sendra J.R., Sevilla D., Villarino C. Covering of surfaces parametrized without projective base points. Proc. ISSAC2014 ACM Press, pages 375-380, 2014,\ud ISBN:978-1-4503-2501-1". http://dx.doi.org/10.1145/2608628.2608635We 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.\ud Moreover, we give explicit formulas for computing the coverings. We provide two di erent approaches: either\ud 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

Covering rational surfaces with rational parametrization images

Let S be a rational projective surface given by means of a projective rational parametrization whose base locus satisfies a mild assumption. In this paper we present an algorithm that provides three rational maps f , g, h : A2 S ⊂ P n such that the union of the three images covers S. As a consequence, we present a second algorithm that generates two rational maps f , g˜ : A2 S, such that the union of its images covers the affine surface S ∩ An . In the affine case, the number of rational maps involved in the cover is in general optimal.Ministerio de Ciencia, Innovación y UniversidadesJ. Caravantes, J.R. Sendra and C. Villarino belong to the Research Group ASYNACS (Ref. CT-CE2019/683). D. Sevilla is a member of the research group GADAC and is partially supported by Junta de Extremadura and FEDER funds (group FQM024)