On the existence of finite surjective parametrizations of affine surfaces

Edoardo Ballico; Claudio Fontanari

On the existence of finite surjective parametrizations of affine surfaces

Algebraic Geometry 2022-03-14 v2

Authors: Edoardo Ballico , Claudio Fontanari

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 $f: \mathbb{A}^2 \to S$ .

Keywords

affine surfaces surjective parametrization finite morphism rational varieties algebraic geometry

Cite

@article{arxiv.2107.11794,
  title  = {On the existence of finite surjective parametrizations of affine surfaces},
  author = {Edoardo Ballico and Claudio Fontanari},
  journal= {arXiv preprint arXiv:2107.11794},
  year   = {2022}
}

Comments

Final version, to appear in J. Algebra

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