On the existence of birational surjective parametrizations of affine surfaces

JOURNAL OF ALGEBRA

卷:501

Article

Caravantes, J.¹  Sendra, J. R.²  Sevilla, D.³  Villarino, C.² 

[1] Univ Complutense Madrid, Res Grp GVP, Dept Algebra, Plaza Ciencias 3, E-28040 Madrid, Spain

[2] Univ Alcala, Dept Fis & Matemat, Res Grp ASYNACS, Alcala De Henares 28871, Madrid, Spain

[3] Univ Extremadura, Ctr U Merida, Res Grp GADAC, Av Santa Teresa de Jornet 38, Merida 06800, Badajoz, Spain

关键词: Rational surface;    Birational parametrization;    Surjective parametrization;   

DOI  :  10.1016/j.jalgebra.2017.12.028

来源: Elsevier

【 摘 要 】

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. (C) 2018 Elsevier Inc. All rights reserved.

【 授权许可】

Free