  The equilibrium points and the curves of zero-velocity (Roche varieties) are
analysed in the frame of the regularized circular restricted three-body
problem. The coordinate transformation is done with Levi-Civita generalized
method, using polynomial functions of n degree. In the parametric plane, five
families of equilibrium points are identified. These families of points
correspond to the five equilibrium points in the physical plane L1, L2, ...,
L5. The zero-velocity curves from the physical plane are transformed in Roche
varieties in the parametric plane. The properties of these varieties are
analysed and the Roche varieties for n = {1,2,...,6} are plotted. The equation
of the asymptotic variety is obtained and its shape is analysed. The slope of
the Roche variety in L11 point is obtained. For n = 1 the slope obtained by
Plavec and Kratochvil (1964) in the physical plane was found.
