$\mathbb{A}^1$-cylinders over smooth $\mathbb{A}^1$-fibered surfaces
Algebraic Geometry
2020-03-02 v1
Abstract
We give a general structure theorem for affine A 1-fibrations on smooth quasi-projective surfaces. As an application, we show that every smooth A 1-fibered affine surface non-isomorphic to the total space of a line bundle over a smooth affine curve fails the Zariski Cancellation Problem. The present note is an expanded version of a talk given at the Kinosaki Algebraic Geometry Symposium in October 2019.
Cite
@article{arxiv.2002.12838,
title = {$\mathbb{A}^1$-cylinders over smooth $\mathbb{A}^1$-fibered surfaces},
author = {Adrien Dubouloz},
journal= {arXiv preprint arXiv:2002.12838},
year = {2020}
}