A linear projection of an algebraic set in $\mathbb{C}^{2}$ is not always algebraic, for instance, the projection of $\{xy=1\}$ on the $x$ axis yields $\mathbb{C}\backslash \{0\}$.
My question is - are there conditions for a projection to be algebraic? Say if all of the fibers have the same dimension? Something more general, or in terms of how $X$ behaves when compared to its projective closure?
Thank you!