Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
8896256 | Journal of Algebra | 2018 | 9 Pages |
Abstract
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.
Keywords
Related Topics
Physical Sciences and Engineering
Mathematics
Algebra and Number Theory
Authors
J. Caravantes, J.R. Sendra, D. Sevilla, C. Villarino,