2017/06/01 by Jorge Caravantes, Caravantes, Jorge, J. Rafael Sendra +5
Computer Science · Engineering · Mathematics · #14Q10 #68W30 #Advanced Numerical Analysis Techniques #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Polynomial and algebraic computation
paper · pdf · doi:10.48550/arxiv.1706.00492
openalex publication_date 2017/06/01 · openalex created_date 2022/10/03 · openalex updated_date 2026/07/28
In this paper we show that not all affine rational complex surfaces can be\nparametrized birationally and surjectively. For this purpose, we prove that, if\nS is an affine complex surface whose projective closure is smooth, a necessary\ncondition for S to admit a birational surjective parametrization from an open\nsubset of the affine complex plane is that the infinity curve of S must contain\nat least one rational component. As a consequence of this result we provide\nexamples of affine rational surfaces that do not admit birational surjective\nparametrizations.\n