Weil-Petersson volume of moduli spaces of curves of low-genus (Q1966242)

Let \({\mathcal M}_{g,n}\) be the moduli space of stable curves of genus \(g\) with \(n\) marked points and let \(V_{g,n}\) denote its volume. Moreover let \(\varphi_g\) be the generating function (for each genus \(g)\) of the Weil-Petersson volume \(\text{Vol}_{WP} ({\mathcal M}_{g,n})\). In this note the author provides some simple formulas expressing \(\varphi_g\), for \(g=1,2\), in terms of the rather explicitly described genus 0 generating function. Then he finds the asymptotic for \(V_{g,n}\) in genus 1 and 2.