Let $X=\mathbb{CP}^n$. We proved using the hodge decomposition that $H^0(X,\Omega^p)=0$ if $p\neq 0$. But I do not understand why I cannot have global holomorphic differential p-forms not even constants.
- I want to understand why $H^0(X,\Omega^p)=0$ without using the Hodge decomposition.
- And without using GAGA I would like to see a proof of $H^0(Proj(\mathbb{C}[x_0,..,x_n]),\Omega_{X/\mathbb{C}}^p)=0$ for $p\neq 0$