  Based on the distinction between the covariant and contravariant metric
tensor components in the framework of the affine geometry approach and the s.c.
"gravitational theories with covariant and contravariant connection and
metrics", it is shown that a wide variety of third, fourth, fifth, seventh,
tenth- degree algebraic equations exists in gravity theory. This is important
in view of finding new solutions of the Einstein's equations, if they are
treated as algebraic ones. Since the obtained cubic algebraic equations are
multivariable, the standard algebraic geometry approach for parametrization of
two-dimensional cubic equations with the elliptic Weierstrass function cannot
be applied. Nevertheless, for a previously considered cubic equation for
reparametrization invariance of the gravitational Lagrangian and on the base of
a newly introduced notion of "embedded sequence of cubic algebraic equations",
it is demonstrated that in the multivariable case such a parametrization is
also possible, but with complicated irrational and non-elliptic functions.
After finding the solutions of a system of first - order nonlinear differential
equations, these parametrization functions can be considered also as
uniformization ones (depending only on the complex uniformization variable z)
for the initial multivariable cubic equation.
