%0 Journal Article 
%A Caravantes Tortajada, Jorge
%A Sendra Pons, Juan Rafael
%A Sevilla, David
%A Villarino Cabellos, Carlos
%T On the existence of birational surjective parametrizations of affine surfaces
%D 2018
%@ 0021-8693
%U http://hdl.handle.net/10017/45758
%X 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.
%K Rational surface
%K Birational parametrization
%K Surjective parametrization
%K Matemáticas
%K Mathematics
%~ Biblioteca Universidad de Alcala