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

Utsav Choudhury, Biman Roy

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 compone…