2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/62904We show that the real-valued function $S_α$ on the moduli space $\mathcal{M}_{0,n}$ of pointed rational curves, defined as the critical value of the Liouville action functional on a hyperbolic 2-sphere with $n\geq 3$ conical singularities of arbitrary orders $α=\{α_1,...,α_n\}$, generates accessory parameters of the associated Fuchsian differential equation as their common antiderivative. We introduce a family of Kaehler metrics on $\mathcal{M}_{0,n}$ parameterized by the set of orders $α$, explictly relate accessory parameters to these metrics, and prove that the functions $S_α$ are their Kaehler potentials.AMS LaTex, 13 pagesComplex VariablesHigh Energy Physics - TheoryDifferential Geometry14H15 (Primary) 30F45, 81T40 (Secondary)text