  For the TZ metric on the moduli space $\mathscr{M}_{0,n}$ of $n$-pointed
rational curves, we construct a K\"ahler potential in terms of the Fourier
coefficients 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 fibers
are 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 $\mathfrak{S}_{g,n}$. We
explicitly compute the Chern forms of these Hermitian line bundles
$$c_{1}(\mathscr{L}_{i},h_{i})=\frac{4}{3}\omega_{\mathrm{TZ},i},\quad
c_{1}(\mathscr{L},\exp\{S/\pi\})=\frac{1}{\pi^{2}}\omega_{\mathrm{WP}}.$$ We
prove that a smooth real-valued function $-\mathscr{S}=-S+\pi\sum_{i=1}^{n}\log
h_{i}$ on $\mathfrak{S}_{g,n}$, a potential for this special difference of WP
and TZ metrics, coincides with the renormalized hyperbolic volume of a
corresponding Schottky $3$-manifold. We extend these results to the
quasi-Fuchsian groups of type $(g,n)$.
