Is the projection map from direct product of projective $n$ space and projective $m$ space to projective $n$ space a closed map?

Question

Is the projection map from direct product of projective $n$ space and projective $m$ space to projective $n$ space a closed map? I know that if $X$, and $Y$ are topological spaces with the product topology on the direct product and if $Y$ is compact then the projection onto $X$ is closed. But the problem here is that the topology on direct product of projective $n$ space and projective $m$ space is not the box topology.

Answer 1

Look for the "Fundamental Theorem of Elimination Theory" in Ravi's notes on algebraic geometry. You can find these here.