Surjective morphisms from affine space to its Zariski open subsets

Abstract

We prove constructively the existence of surjective morphisms from affine space onto certain open subvarieties of affine space of the same dimension. For any algebraic set $Z\subset {\mathbb{A}}^{n-2}\subset {\mathbb{A}}^n$, we construct an endomorphism of ${\mathbb{A}}^n$ with ${\mathbb{A}}^n\setminus Z$ as its image. By Noether's normalization lemma, these results extend to give surjective maps from any $n$-dimensional affine variety $X$ to ${\mathbb{A}}^n\setminus Z$.

7 pages. v2, typos corrected. Accepted for publication in IJM

References in corpus (1)

• On images of affine spaces

Cited by in corpus (2)

• Algebraic Gromov ellipticity: a brief survey
• Affine cones as images of affine spaces