$\mathbb{A}^1$-connected components and characterisation of $\mathbb{A}^2$

Utsav Choudhury; Biman Roy

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arXiv · 2112.13089

$\mathbb{A}^1$-connected components and characterisation of $\mathbb{A}^2$

Utsav Choudhury·Biman Roy

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Abstract

In this article we prove that any $\mathbb{A}^1$-contractible smooth complex surface is isomorphic as a variety to $\mathbb{C}^2$. We show that the $\mathbb{A}^1$-connected component of a variety $X$ contains the information about $\mathbb{A}^1$'s in $X$.

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BibTeX RIS

Utsav Choudhury, Biman Roy. 2021-12-24. $\mathbb{A}^1$-connected components and characterisation of $\mathbb{A}^2$. https://arxiv.org/abs/2112.13089

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