Saved in:
| Main Author: | |
|---|---|
| Format: | Preprint |
| Published: |
2025
|
| Subjects: | |
| Online Access: | https://arxiv.org/abs/2512.06687 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
Table of Contents:
- Let $X$ be a factorial complex affine variety of dimension $\ge 3$ with an algebraic action of the additive group $G_a$. Let $π: X \to Y$ be the algebraic quotient morphism where we assume $Y$ is an affine variety. When $π$ is faithfully flat, we investigate $π$ by $G_a$-equivariant affine modifications and give criteria for $π$ to be a trivial $\mathbb A^1$-bundle. For a smooth acyclic fourfold $X$ with a free $G_a$-action and a $G_a$-equivariant $\mathbb A^3$-fibration $f : X \to \mathbb A^1$ where $G_a$ acts trivially on $\mathbb A^1$, we give a criterion for the algebraic quotient $Y$ to be isomorphic to $\mathbb A^3$ with $f$ as a coordinate. Together with a criterion for $π: X \to Y$ to be a trivial $\mathbb A^1$-bundle, we obtain a sufficient condition for $X\cong Y\times \mathbb A^1\cong \mathbb A^4$.