  We show that a smooth Moishezon space $Y$ is non-projective if and only if it
contains a rational curve such that $-[C] \in \overline{\mathrm{NE}}(Y)$. More
generally, this holds if $Y$ has $\mathbb{Q}$-factorial, log terminal
singularities. We derive this as a consequence of our main technical result:
that we can run the relative minimal model program when the base is a normal
algebraic space $Y$ of finite type over a field of characteristic $0$. As a
second application, we show that every log canonical pair $(Y, \Delta)$, where
$Y$ is an algebraic space of finite type over a field of characteristic $0$
admits a dlt modification that is projective over $Y$.
