The generating function that gives rise to the orbifold Euler characteristic of the moduli space of punctured compact Rieman surfaces [Formula: see text], g ≥ 0 is derived explicitly. In the derivation, we show that we do not need to use the three-term recursion relation for the orthogonal polynomials. Also the continuum limit of Penner's connected generating function is considered and is shown to be formally equivalent to the free energy obtained recently by Distler and Vafa which exhibits the logarithmic divergences found for genus zero and one in D = 1 matrix models. Finally, it is shown that the free energy and its s-derivatives are nothing but the continuum limit of a certain generating function introduced by Harer and Zagier in obtaining the true Euler characteristic with any number of punctures,[Formula: see text], s ≥ 0.
The Chow ring of the moduli space of curves of genus zero
