Covering Rational Surfaces with Rational Parametrization Images

descriptionPublicationkeyboard_double_arrow_right Article , Preprint , Other literature type 08 Feb 2021Embargo end date: 01 Jan 2021 Spain English Publisher:MDPI AGJournal:Mathematics, volume 9, page 338 (eissn: 2227-7390,

Copyright policy )

Authors: Caravantes Tortajada, Jorge; Sendra Pons, Juan Rafael; Sevilla, David; Villarino Cabellos, Carlos;

doi: 10.3390/math9040338 , 10.48550/arxiv.2101.07011

arXiv: 2101.07011

handle: 10017/49642

Covering Rational Surfaces with Rational Parametrization Images

- Summary
- Subjects
- Metrics

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:A2⇢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˜: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.

Country

Spain

Related Organizations

University of Extremadura
Spain
University of Alcalá
Spain

Keywords

Computer Science - Symbolic Computation, FOS: Computer and information sciences, Base points, surface cover, Surface cover, Matemáticas, Symbolic Computation (cs.SC), birational parametrization, Surjective parametrization, Mathematics - Algebraic Geometry, base points, QA1-939, FOS: Mathematics, 14Q10 (Primary) 68W30 (Secondary), Rational surface, Birational parametrization, rational surface, surjective parametrization, Algebraic Geometry (math.AG), Mathematics

Impact byBIP!

	selected citations These citations are derived from selected sources. This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).	2
	popularity This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.	Average
	influence This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).	Top 10%
	impulse This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.	Average