On the existence of birational surjective parametrizations of affine surfaces
Autores
Caravantes Tortajada, Jorge; Sendra Pons, Juan Rafael; Sevilla, David; Villarino Cabellos, CarlosIdentificadores
Enlace permanente (URI): http://hdl.handle.net/10017/45758DOI: 10.1016/j.jalgebra.2017.12.028
ISSN: 0021-8693
Editor
Elsevier
Fecha de publicación
2018-05-01Patrocinadores
Ministerio de Economía y Competitividad
Junta de Extremadura
Cita bibliográfica
Caravantes, J., Sendra, J.R., Sevilla, D. & Villarino, C. 2018, "On the existence of birational surjective parametrizations of affine surfaces", Journal of Algebra, vol. 501, pp. 206-214.
Palabras clave
Rational surface
Birational parametrization
Surjective parametrization
Proyectos
info:eu-repo/grantAgreement/MINECO//MTM2014-54141-P/ES/CONSTRUCCIONES ALGEBRO-GEOMETRICAS: FUNDAMENTOS, ALGORITMOS Y APLICACIONES/
FQM024 (Junta de Extremadura y FEDER)
Tipo de documento
info:eu-repo/semantics/article
Versión
info:eu-repo/semantics/acceptedVersion
Versión del editor
https://doi.org/10.1016/j.jalgebra.2017.12.028Derechos
Attribution-NonCommercial-NoDerivatives 4.0 Internacional
© 2018 Elsevier
Derechos de acceso
info:eu-repo/semantics/openAccess
Resumen
In this paper we show that not all affine rational complex surfaces can be parametrized birational and surjectively. For this purpose, we prove that, if S is an affine complex surface whose projective closure is smooth, a necessary condition for S to admit a birational surjective parametrization from an open subset of the affine complex plane is that the curve at infinity of S must contain at least one rational component. As a consequence of this result we provide examples of affine rational surfaces that do not admit birational surjective parametrizations.
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Colecciones
- MATEMATIC - Artículos [172]