On the existence of birational surjective parametrizations of affine surfaces
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 fro...
| Autores: | , , , |
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| Tipo de recurso: | artículo |
| Fecha de publicación: | 2018 |
| País: | España |
| Institución: | Universidad de Alcalá (UAH) |
| Repositorio: | e_Buah Biblioteca Digital Universidad de Alcalá |
| Idioma: | inglés |
| OAI Identifier: | oai:ebuah.uah.es:10017/45758 |
| Acceso en línea: | http://hdl.handle.net/10017/45758 https://dx.doi.org/10.1016/j.jalgebra.2017.12.028 |
| Access Level: | acceso abierto |
| Palabra clave: | Rational surface Birational parametrization Surjective parametrization Matemáticas Mathematics |
| Sumario: | 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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