# algebraic geometry – Action of \$PGL_2\$ on \$mathbb{P}^n\$

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.