A one-parameter family of algebraic curves has an
envelope line, which may be imaginary in certain cases. Jakob
Steiner was right, considering the imaginary images as creation of
analysis. In the analysis a real number is just a part of a complex
number and in certain conditions the initial real values can give an
imaginary result. But Steiner was wrong in denying the imaginary
images in geometry. The geometry, in contrast to the single analytical
space exists in several spaces: Euclidean geometry operates
only on real figures valid and does not contain imaginary figures
by definition; pseudo-Euclidean geometry operates on imaginary
images and constructs their images, taking into account its own
features. Geometric space is complex and each geometric object in
it is the complex one, consisting of the real figure (core) having the
"aura" of an imaginary extension. Thus, any analytical figure of the
plane is present at every point of the plane or by its real part or by
its imaginary extension. Would the figure’s imaginary extension be
visible or not depends on the visualization method, whether the
image has been assumed on superimposed epures – the Euclideanpseudo-Euclidean
plane, or the image has been traditionally assumed
only in the Euclidean plane. In this paper are discussed cases when
a family of algebraic curves has an envelope, and is given an answer
to a question what means cases of complete or partial absence of
the envelope for the one-parameter family of curves. Casts some
doubt on widely known categorical st
Families of Algebraic Varieties and Towers of Algebraic Curves over Finite Fields