Covering Rational Surfaces with Rational Parametrization Images

Jorge Caravantes, J. Rafael Sendra, David Sevilla and Carlos Villarino
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Jorge Caravantes: Department of Physics and Mathematics, The University of Alcalá, 28801 Alcalá de Henares, Madrid, Spain
J. Rafael Sendra: Department of Physics and Mathematics, The University of Alcalá, 28801 Alcalá de Henares, Madrid, Spain
David Sevilla: Department of Mathematics, The University of Extremadura, 06800 Mérida, Badajoz, Spain
Carlos Villarino: Department of Physics and Mathematics, The University of Alcalá, 28801 Alcalá de Henares, Madrid, Spain

Mathematics, 2021, vol. 9, issue 4, 1-15

Abstract: 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 , g ˜ : A 2 ? S , such that the union of its 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.

Keywords: rational surface; birational parametrization; surjective parametrization; surface cover; base points (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2021
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