I understand that $CP^1$ is the Riemann Sphere. I guess all its discrete symmetries were known for a long time and well-classified. (But suggestions or good references where this is worked out in a neat way would be appreciated.)

My question is: I want to know about the discrete symmetries of $CP^2$ and more generally, also $CP^n$. Is there any place these are worked out in a simple way?

Are there any classical references specifically about the complex projective plane?