Is there a reference showing that the space $\bar{M_{g,n}}$ is a closed oriented orbifold and it is hausdorffHausdorff? Note: here $\bar{M_{g,n}}$ is not the Deligne-Mumford space in the usual algebraic geometry, ; it consists of is the moduli space for smooth or nodal Riemann surface surfaces with genus $g$ and $n$ marked smooth points and such that it satisfies the stability condition. Thanks!
# Is there a reference showing that the space $\bar{M_{g,n}}$ is a closed oriented orbifold and it is hausdorff
Is there a reference showing that the space $\bar{M_{g,n}}$ is a closed oriented orbifold and it is hausdorff? Note: here $\bar{M_{g,n}}$ is not Deligne-Mumford space in the usual algebraic geometry, it consists of smooth or nodal Riemann surface with genus $g$ and $n$ marked smooth points and satisfies stability condition. Thanks!