2 Changed $\phi$ to be regular map on complement of $x$.
Let $k$ be an algebraically closed infinite field, and consider some subscheme $X\subset \mathbb{P}_k^n$. Let $x$ be a closed point of $X$, and $H$ a general hyperplane containing $x$. There is a rational regular map $\phi:\mathbb{P}^n\dashrightarrow \phi:\mathbb{P}^n\setminus{{x}}\rightarrow \mathbb{P}^{n-1}$ gotten by projecting from the point $x$.