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 the Deligne-Mumford space in the usual algebraic geometry; it is the moduli space for smooth or nodal Riemann surfaces with genus $g$ and $n$ marked smooth points such that it satisfies the stability condition. Thanks!

edited Jul 5 2010 at 3:21

BCnrd
4,116●1●38●58

asked Jul 5 2010 at 0:39

HYYY
923●4●10

Dude, you're asking too many variants of the same question (and too many question overall in one day: please give people a chance to respond to what you already wrote). I wrote a long comment to answer this in response to your earlier question, so you can cancel this question. – BCnrd Jul 5 2010 at 1:26

mathabc -- what do you mean by the stability condition? And what is the "usual algebraic geometry"? – algori Jul 5 2010 at 1:38

@algori: mathabc means each fiber satisfies the condition as in the definition of a stable marked curve as in the moduli problem which defines the usual Deligne-Mumford moduli stack. By "usual algebraic geometry", mathabc is emphasizing that the question concerns a moduli problem defined entirely within the complex-analytic category, not tautologically asking about the analytification of the algebraic DM-stack (so the hard part is to rigorously prove that the algebraic moduli stack does analytify to the moduli stack for the analytic category; this is not a matter of mere definitions). – BCnrd Jul 5 2010 at 1:51

BCnrd -- thanks, this has clarified things for me. I find the presentation in the posting a bit too compressed. – algori Jul 5 2010 at 1:58

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