On images of affine spaces

TL;DR

This paper proves that various algebraic varieties, including non-degenerate toric varieties and homogeneous spaces, can be obtained as images of affine spaces via surjective morphisms, revealing their affine space structures.

Contribution

It establishes the existence of surjective morphisms from affine spaces to a broad class of algebraic varieties, extending understanding of their geometric structures.

Findings

Surjective morphisms from affine spaces to non-degenerate toric varieties exist.

Homogeneous spaces of certain algebraic groups admit affine space images.

Varieties covered by affine spaces can be obtained from affine spaces via surjective maps.

Abstract

We prove that every non-degenerate toric variety, every homogeneous space of a connected linear algebraic group without non-constant invertible regular functions, and every variety covered by affine spaces admits a surjective morphism from an affine space.