Hello,


Does any proper morphism $X \to Y$ of, say, algebraic varieties, can be factored as $X \to Z \times Y \to Y$, where $X \to Z \times Y$ is a closed embedding, and $Z \times Y \to Y$ is the projection (and $Z$ is complete).


I ask just out of curiosity.


Sasha



Decomposition of a proper morphism
By Nagata's theorem there is an open immersion $j:X\hookrightarrow \overline{X}$ where $\overline{X}$ is complete. Then, as ABayer suggests, take $(j,f): \overline{X}\times Y$.


