I am just curious about something.
The asymptotic cone of $\mathbb{Z}^n$ minus one point is $\mathbb{R}^n$. In fact, I think the asymptotic cone of $\mathbb{Z}^n$ minus a finite number of points is still $\mathbb{R}^n$.
So would the asymptotic cone of $GL_n(k)$ equal to the set of all matrices $M_n(k)$, where $k$ is algebraically closed?
And would the asymptotic cone of unipotent matrices in $GL_n(k)$ equal to itself?
Thanks for your time.