${\mathbb{A}}^1$-homotopy type of ${\mathbb{A}}^2\setminus \left\{(0,0)\right\}$

Utsav Choudhury, Biman Roy

In this article we prove that any ${\mathbb{A}}^1$-connected smooth $k$-variety is ${\mathbb{A}}^1$-uniruled for any algebraically closed field $k$. We establish that if a non empty op…