  Let $\mathfrak g$ be an infinite-dimensional Lie algebra, and $G$ be the
algebraic completion of a $\mathfrak g$-module. Using the geometric model of
Schottky uniformization of Riemann sphere to obtain a higher genus Riemann
surface, we construct a family of parametric extensions of coboundary operators
for the double complexes of meromorphic functions depending on elements of $G$,
and possessing prescribed analytic properties.
