On the existence of finite surjective parametrizations of affine surfaces

2021/07/25 by Ballico, Edoardo, Fontanari, Claudio
#Algebraic Geometry (math.AG) #FOS: Mathematics

paper · doi:10.48550/arxiv.2107.11794

Abstract

We investigate surjective parametrizations of rational algebraic varieties, in the vein of recent work by Jorge Caravantes, J. Rafael Sendra, David Sevilla, and Carlos Villarino. In particular, we show how to construct plenty of examples of affine surfaces S not admitting a finite surjective morphism f: \mathbbA² → S.

Related

• On the existence of birational surjective parametrizations of affine\n surfaces
• Affine equivalences, isometries and symmetries of ruled rational surfaces
• Covering rational surfaces with rational parametrization images
• Covering Rational Ruled Surfaces
• Relative forms of real algebraic varieties and examples of quasi-projective surfaces with algebraic moduli of real forms