  One can consider the Hilbert scheme as a natural compactification of the
space of smooth projective curves with fixed Hilbert polynomial. Here we
consider a different modular compactification, namely the functor CM
parameterizing curves together with a finite map to $\mathbb{P}^n$ that is
generically a closed immersion.
  We prove that CM is an algebraic space by contructing a scheme W and a
representable, surjective and smooth map W -> CM. Moreover, we show that CM
satisfies the valuative criterion for properness.
