Hyperbolic 2-spheres with conical singularities, accessory parameters and Kaehler metrics on ${\mathcal{M}}_{0,n}$

Leon Takhtajan, Peter Zograf

We show that the real-valued function $S_{\alpha }$ on the moduli space ${\mathcal{M}}_{0,n}$ of pointed rational curves, defined as the critical value of the Liouville action functional on…