I was trying to prove that the meromorphic function on the projective n space $\Bbb{CP}^n $ is rational (without using Chow's theorem).
To do this we needs to use the fact that the meromorphic function on the projective line is rational.(which is a standard result in Riemann surface theory).
To apply this result , we needs to fixed all the variable and left one variable varies (one variable at a time ), however, I have not idea how to fix variables in projective coordinate $[x_0:...:x_{n+1}]$