Covering rational surfaces with rational parametrization images

01/18/2021

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by   Jorge Caravantes, et al.

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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:𝔸^2 –→ 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,g̃:𝔸^2 –→ S, such that the union of their images covers the affine surface S∩𝔸^n. In the affine case, the number of rational maps involved in the cover is in general optimal.