𝔸¹-connected components and characterisation of 𝔸²

Abstract

In this article, we prove that any

-contractible smooth complex surface is isomorphic as a variety to

C 2 \mathbb{C}^{2}

. We show that the

A 1 \mathbb{A}^{1}

-connected component of a variety 𝑋 contains the information about

A 1 \mathbb{A}^{1}

’s in 𝑋.