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For the TZ metric on the moduli space $\mathscr{M}_{0,n}$ of $n$-pointedrational curves, we construct a K\"ahler potential in terms of the Fouriercoefficients of the Klein's Hauptmodul. We define the space$\mathfrak{S}_{g,n}$ as holomorphic fibration$\mathfrak{S}_{g,n}\rightarrow\mathfrak{S}_{g}$ over the Schottky space$\mathfrak{S}_{g}$ of compact Riemann surfaces of genus $g$, where the fibersare configuration spaces of $n$ points. For the tautological line bundles$\mathscr{L}_{i}$ over $\mathfrak{S}_{g,n}$ we define Hermitian metrics $h_{i}$in terms of Fourier coefficients of a covering map $J$ of the Schottky domain.We define the regularized classical Liouville action $S$ and show that$\exp\{S/\pi\}$ is a Hermitian metric in the line bundle$\mathscr{L}=\otimes_{i=1}^{n}\mathscr{L}_{i}$ over $\mathfrak{S}_{g,n}$. Weexplicitly compute the Chern forms of these Hermitian line bundles$$c_{1}(\mathscr{L}_{i},h_{i})=\frac{4}{3}\omega_{\mathrm{TZ},i},\quadc_{1}(\mathscr{L},\exp\{S/\pi\})=\frac{1}{\pi^{2}}\omega_{\mathrm{WP}}.$$ Weprove that a smooth real-valued function $-\mathscr{S}=-S+\pi\sum_{i=1}^{n}\logh_{i}$ on $\mathfrak{S}_{g,n}$, a potential for this special difference of WPand TZ metrics, coincides with the renormalized hyperbolic volume of acorresponding Schottky $3$-manifold. We extend these results to thequasi-Fuchsian groups of type $(g,n)$.

Potentials and Chern forms for Weil-Petersson and Takhtajan-Zograf metrics on moduli spaces