Katharina Heinrich: The Space of Cohen-Macaulay Curves

In this thesis we discuss a moduli space of projective curves with a map to a given projective space. The functor CM parametrizes curves, that is, Cohen-Macaulay schemes of pure dimension 1, together with a finite map to the projective space that is an isomorphism onto its image away from a finite set of closed points.

We prove that CM is an algebraic space by constructing a scheme W and a representable, surjective and smooth map from W to CM.