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arXiv · 2002.12838

$\mathbb{A}^1$-cylinders over smooth $\mathbb{A}^1$-fibered surfaces

Adrien Dubouloz
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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.

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Adrien Dubouloz. 2020-02-28. $\mathbb{A}^1$-cylinders over smooth $\mathbb{A}^1$-fibered surfaces. https://arxiv.org/abs/2002.12838

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