I am studying Fulton and Harris’ book and in the chapter “Geometric Plethysm” they talk about how the action of $PGL_2$ on $mathbb{P}^n$ fixes the rational normal curve $C$ of degree $n$. But I have an extremely basic confusion, namely what is said action of $PGL_2$ on $mathbb{P}^n$? I don’t see any obvious candidates.

I guess that if this is resolved I will be able to see why it fixes $C$. I tried to work backwards from the fact that it fixes $C$ to find the action but no luck there.