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 $Z\subset {𝔸}^{n-2}\subset {𝔸}^n$, we construct an endomorphism of ${𝔸}^n$ with ${𝔸}^n\setminus Z$ as its image. By Noether’s normalization lemma, these results extend to give surjective maps from any $n$-dimensional affine variety $X$ to ${𝔸}^n\setminus Z$.

中文翻译：

---

从仿射空间到其 Zariski 开子集的满射态射

我们建设性地证明了从仿射空间到相同维度的仿射空间的某些开子族的满射态射的存在。对于任意代数集$Z\subset {𝔸}^{n-2}\subset {𝔸}^n$，我们构造一个自同态${𝔸}^n$和${𝔸}^n\setminus Z$作为它的形象。根据诺特的归一化引理，这些结果扩展到给出任意的满射映射$n$维仿射簇$X$到${𝔸}^n\setminus Z$。