$\mathbb{A}^1$-cylinders over smooth $\mathbb{A}^1$-fibered surfaces - Archive ouverte HAL Accéder directement au contenu
Autre Publication Scientifique Kinosaki Algebraic Geometry Symposium Année : 2020

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

Résumé

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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Dates et versions

hal-02492470 , version 1 (27-02-2020)

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Citer

Adrien Dubouloz. $\mathbb{A}^1$-cylinders over smooth $\mathbb{A}^1$-fibered surfaces. Proceedings of Kinosaki Algebraic Geometry Symposium (2019), 2020, p. 95-103. ⟨hal-02492470⟩
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