RT info:eu-repo/semantics/article
T1 On the existence of birational surjective parametrizations of affine surfaces
A1 Caravantes Tortajada, Jorge
A1 Sendra Pons, Juan Rafael
A1 Sevilla, David
A1 Villarino Cabellos, Carlos
K1 Rational surface
K1 Birational parametrization
K1 Surjective parametrization
K1 Matemáticas
K1 Mathematics
AB 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.
PB Elsevier
SN 0021-8693
YR 2018
FD 2018-05-01
LK http://hdl.handle.net/10017/45758
UL http://hdl.handle.net/10017/45758
LA eng
NO Ministerio de Economía y Competitividad
DS MINDS@UW
RD 26-abr-2024