Computation of the degree of rational surface parametrizations
Identifiers
Permanent link (URI): http://hdl.handle.net/10017/49505DOI: 10.1016/j.jpaa.2004.02.011
ISSN: 0022-4049
Publisher
Elsevier
Date
2004-10-01Bibliographic citation
Pérez Díaz, S. & Sendra, J.R. 2004, "Computation of the degree of rational surface parametrizations", Journal of Pure and Applied Algebra, vol. 193, no. 1-3, pp. 99-121.
Keywords
Rational Parametrization
Algebraic Surface
Degree of a Rational Map
Project
BMF2002-04402-C02-01
HU2001-0002
GAIA II (IST-2002-35512)
Document type
info:eu-repo/semantics/article
Version
info:eu-repo/semantics/publishedVersion
Publisher's version
https://doi.org/10.1016/j.jpaa.2004.02.011Rights
Attribution-NonCommercial-NoDerivatives 4.0 International (CC BY-NC-ND 4.0)
© 2003 Elsevier
Access rights
info:eu-repo/semantics/openAccess
Abstract
A rational affine parametrization of an algebraic surface establishes a rational correspondence of the affine plane with the surface. We consider the problem of computing the degree of such a rational map. In general, determining the degree of a rational map can be achieved by means of elimination theoretic methods. For curves, it is shown that the degree can be computed by gcd computations. In this paper, we show that the degree of a rational map induced by a surface parametrization can be computed by means of gcd and univariate resultant computations. The basic idea is to express the elements of a generic fibre as the finitely many intersection points of certain curves directly constructed from the parametrization, and defined over the algebraic closure of a field of rational functions.
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