Abstract
Letgdenote the moduli space of compact Riemann surfaces of genusg> 3. It is known thatgis a non-complete quasi-projective variety that contains many complete curves. This is because the Satake compactificationgofgis projective and the boundary\has co-dimension 2; thus by intersectingwith hypersurfaces in sufficiently general position one obtains a complete curve ingpassing through any given set of points [8].
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