Abstract
The known restrictions on the disposition of ovals of a nonsingular projective real algebraic curve leave possible for M-curves of degree 10 about 70,000 real schemes. These schemes divide naturally into 18 families. Basic result: in each of these families there exist representatives realizing M-curves of degree 10. Using the method of O. Ya. Viro, based on perturbations of curves with involved singularities, there are constructed more than 500 M-curves of degree 10. Incidentally there are obtained a large number of perturbations of points of tangency of five branches.
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