Affine curves of degree 6 and smoothings of a nondegenerate sixth order singular point

The paper is devoted to an isotopic classification of plane nonsingular real affine curves of degree 6 with maximum number of ovals (ten) and to the establishment of a connection between these curves and smoothings (nonsingular perturbations) of a nondegenerate sixth order singular point. Of 120 isotopic types admissible by known restrictions, 32 types are realized and 69 types are prohibited. It is proved that every smoothing of a nondegenerate sixth order singular point is the image of an affine curve of degree 6 under a homomorphism of the plane onto a neighborhood of the singular point.
Bibliography: 28 titles.