Riemann existence theorem and construction of real algebraic curves
by S.Yu. Orevkov
Abstract
In this paper we propose a method of construction of plane
real algebraic curves
given by f( x, y ) = 0,
deg_y( f ) = 3
which has a required arrangement on the affine plane with respect to
the pencil of vertical lines.
The methode is base on the techniques of "dessins d'enfant".
As an illustration, we give a construction of a new complex
scheme of projective M-curve of degree 7 and a construction
of 66 new isotopy types of M-curves of degree 9.