DOI: 10.1142/s0129167x23500751 ISSN:

Surjective morphisms from affine space to its Zariski open subsets

Viktor Balch Barth
  • General Mathematics

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 [Formula: see text], we construct an endomorphism of [Formula: see text] with [Formula: see text] as its image. By Noether’s normalization lemma, these results extend to give surjective maps from any [Formula: see text]-dimensional affine variety [Formula: see text] to [Formula: see text].

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