# Extend any morphism to suitable projective variety? [closed]

Let $$F: X\to \mathbb{P}^n$$ be a morphism from an affine variety to projective space (over some algebraically closed field of characteristic zero). Can we always find an open immersion $$\iota: X\hookrightarrow\tilde{X}$$ to some projective variety $$\tilde{X}$$ such that there is a morphism $$\tilde{F}:\tilde{X}\to\mathbb{P}^n$$ that extends $$F$$, i.e. $$F=\tilde{F}\circ\iota$$? The intuition says that this should be possible using blow-ups but I haven't found a suitable reference.

## closed as off-topic by abx, LSpice, user44191, Dima Pasechnik, Stanley Yao XiaoJul 14 at 19:24

This question appears to be off-topic. The users who voted to close gave this specific reason:

• "This question does not appear to be about research level mathematics within the scope defined in the help center." – LSpice, user44191, Dima Pasechnik, Stanley Yao Xiao
If this question can be reworded to fit the rules in the help center, please edit the question.

• Consider the graph $\Gamma \subset X\times \mathbb{P}^n$ of $F$ — it is isomorphic to $X$. Embed $X$ into some projective space $\mathbb{P}$, and take for $\tilde{X}$ the closure of $\Gamma$ in $\mathbb{P}\times \mathbb{P}^n$. – abx Jul 8 at 13:59