Geodesic
Affine curves of degree~6 and smoothings of a~nondegenerate sixth order singular point
Izvestiya. Mathematics , Tome 33 (1989) no. 3, pp. 501-520

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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. 
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     author = {A. B. Korchagin and E. I. Shustin},
     title = {Affine curves of degree~6 and smoothings of a~nondegenerate sixth order singular point},
     journal = {Izvestiya. Mathematics },
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A. B. Korchagin; E. I. Shustin. Affine curves of degree~6 and smoothings of a~nondegenerate sixth order singular point. Izvestiya. Mathematics , Tome 33 (1989) no. 3, pp. 501-520. http://geodesic.mathdoc.fr/item/IM2_1989_33_3_a2/