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Covering Rational Surfaces with Rational Parametrization Images

Author

Listed:
  • 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)

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.

Suggested Citation

  • Jorge Caravantes & J. Rafael Sendra & David Sevilla & Carlos Villarino, 2021. "Covering Rational Surfaces with Rational Parametrization Images," Mathematics, MDPI, vol. 9(4), pages 1-15, February.
    • Handle: RePEc:gam:jmathe:v:9:y:2021:i:4:p:338-:d:495630
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