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

Utsav Choudhury; Biman Roy

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

Algebraic Geometry 2023-11-09 v4

Authors: Utsav Choudhury , Biman Roy

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 $X$ .

Keywords

projective varieties

Cite

@article{arxiv.2112.13089,
  title  = {$\mathbb{A}^1$-connected components and characterisation of $\mathbb{A}^2$},
  author = {Utsav Choudhury and Biman Roy},
  journal= {arXiv preprint arXiv:2112.13089},
  year   = {2023}
}

Comments

Proof of almost all the main theorems remain same. Corrected several typos and citations. Changed the title. Theorem 1.1 is true now in characteristic 0

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