Computation of the degree of rational surface parametrizations
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 t...
| Autores: | , |
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| Tipo de recurso: | artículo |
| Fecha de publicación: | 2004 |
| País: | España |
| Institución: | Universidad de Alcalá (UAH) |
| Repositorio: | e_Buah Biblioteca Digital Universidad de Alcalá |
| Idioma: | inglés |
| OAI Identifier: | oai:ebuah.uah.es:10017/49505 |
| Acceso en línea: | http://hdl.handle.net/10017/49505 https://dx.doi.org/10.1016/j.jpaa.2004.02.011 |
| Access Level: | acceso abierto |
| Palabra clave: | Rational Parametrization Algebraic Surface Degree of a Rational Map Matemáticas Mathematics |
| Sumario: | 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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