Geodesic
On the topology of planar real decomposable curves of degree~8
Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Proceedings of the XVII All-Russian Youth School-Conference «Lobachevsky Readings-2018», November 23-28, 2018, Kazan. Part 2, Tome 176 (2020), pp. 3-18

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We consider the problem of topological classification of arrangements in the real projective plane of the union of nonsingular curves of degrees $2$ and $6$ under certain conditions of maximality and general position. We list admissible topological models of such arrangements to be studied by using the Orevkov method based on the theory of braids and links and prove that most of these models cannot be realized by curves of degree $8$.
Mots-clés : $M$-decomposable curve
Keywords: topological classification, Orevkov method. 
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     author = {I. M. Borisov and G. M. Polotovsky},
     title = {On the topology of planar real decomposable curves of degree~8},
     journal = {Itogi nauki i tehniki. Sovremenna\^a matematika i e\"e prilo\v{z}eni\^a. Temati\v{c}eskie obzory},
     pages = {3--18},
     publisher = {mathdoc},
     volume = {176},
     year = {2020},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/INTO_2020_176_a0/}
}
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I. M. Borisov; G. M. Polotovsky. On the topology of planar real decomposable curves of degree~8. Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Proceedings of the XVII All-Russian Youth School-Conference «Lobachevsky Readings-2018», November 23-28, 2018, Kazan. Part 2, Tome 176 (2020), pp. 3-18. http://geodesic.mathdoc.fr/item/INTO_2020_176_a0/