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I wanted to know how can I estimate the volume of the moduli space of a Riemann surface of genus $g$ and having $n$ marked points. I am reading some old string theory papers which discuss divergences in string perturbation theory. In this respect authors such as Gross, Periwal and Shenker say that the partition function in closed bosonic string theories asymptotically grows as $(2g)!$, where $g$ is the genus and they claim that this estimate can be obtained from the volume of moduli space. It would be great if anyone of you can suggest some reference where I learn about finding out the volume of moduli space of genus-$g$ surfaces with $n$ punctures.

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    $\begingroup$ Perhaps this question should (also?) be asked on math.SE? $\endgroup$ – Danu Sep 5 '14 at 7:22
  • $\begingroup$ If I remember correctly this is discussed somewhere in the chapter "String interactions and Riemann surfaces" from Zwiebach's A first course in String Theory book. $\endgroup$ – Heterotic Sep 6 '14 at 12:10
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    $\begingroup$ A pointer to a good reference is given here. $\endgroup$ – Dilaton Sep 8 '14 at 1:38

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