Covering rational surfaces with rational parametrization images

2021/01/18 by Caravantes, Jorge, Sendra, J. Rafael, Sevilla, David +1
#14Q10 (Primary) 68W30 (Secondary) #Algebraic Geometry (math.AG) #FOS: Computer and information sciences #FOS: Mathematics #Symbolic Computation (cs.SC)

paper · doi:10.48550/arxiv.2101.07011

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:\mathbbA² --→ S⊂ ℙⁿ 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:\mathbbA² --→ S, such that the union of their images covers the affine surface S∩ \mathbbAⁿ. In the affine case, the number of rational maps involved in the cover is in general optimal.

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